Statistical Tests for Joint Analysis of Performance Measures

Recently there has been an increasing interest in the development of new methods using Pareto optimality to deal with multi-objective criteria (for example, accuracy and architectural complexity). Once one has learned a model based on their devised method, the problem is then how to compare it with the state of art. In machine learning, algorithms are typically evaluated by comparing their performance on different data sets by means of statistical tests. Unfortunately, the standard tests used for this purpose are not able to jointly consider performance measures. The aim of this paper is to resolve this issue by developing statistical procedures that are able to account for multiple competing measures at the same time. In particular, we develop two tests: a frequentist procedure based on the generalized likelihood-ratio test and a Bayesian procedure based on a multinomial-Dirichlet conjugate model. We further extend them by discovering conditional independences among measures to reduce the number of parameter of such models, as usually the number of studied cases is very reduced in such comparisons. Real data from a comparison among general purpose classifiers is used to show a practical application of our tests.

The brain-sex theory of occupational choice: a counterexample

The brain-sex theory of occupational choice suggests that males and females in male-typical careers show a male pattern of cognitive ability in terms of better spatial than verbal performance on cognitive tests with the reverse pattern for females and males in female-typical careers, These differences are thought to result from patterns of cerebral functional lateralisation. This study Sought Such occupationally related effects using synonym generation (verbal ability) and mental rotation (spatial ability) tasks used previously. It also used entrants to these careers as participants to examine whether patterns of cognitive abilities might predate explicit training and practice. Using a population of entrants to sex-differentiated University Courses, a moderate occupational effect on the synonym generation task was found, along with a weak (p<.10) sex effect on the mental rotation task. Highest performance on the mental rotation task was by female Students in fashion design, a female-dominated occupation which makes substantial visuospatial demands and attracts many students with literacy problems such as dyslexia. This group then appears to be a counterexample to the brain-sex theory. However, methodological issues Surrounding previous Studies are highlighted: the simple synonym task appears to show limited discrimination of the sexes, leading to questions concerning the legitimacy of inferences about lateralisation based on scores from that test. Moreover, the human figure-based mental rotation task appears to tap the wrong aspect of visuospatial skill, likely to be needed for male-typical courses such as engineering, Since the fashion-clesign career is also one that attracts disproportionately many male students whose sexual orientation is homosexual, data were examined for evidence of female-typical patterns of cognitive performance among that subgroup. This was not found. This study therefore provides Do evidence for the claim that female-pattern cerebral functional lateralisation is likely in gay males.

On the choice of posittioning and cluster size for fixed relay stations in a LTE network

The long term evolution (LTE) is one of the latest standards in the mobile communications market. To achieve its performance, LTE networks use several techniques, such as multi-carrier technique, multiple-input-multiple-output and cooperative communications. Inside cooperative communications, this paper focuses on the fixed relaying technique, presenting a way for determining the best position to deploy the relay station (RS), from a set of empirical good solutions, and also to quantify the associated performance gain using different cluster size configurations. The best RS position was obtained through realistic simulations, which set it as the middle of the cell's circumference arc. Additionally, it also confirmed that network's performance is improved when the number of RSs is increased. It was possible to conclude that, for each deployed RS, the percentage of area served by an RS increases about 10 %. Furthermore, the mean data rate in the cell has been increased by approximately 60 % through the use of RSs. Finally, a given scenario with a larger number of RSs, can experience the same performance as an equivalent scenario without RSs, but with higher reuse distance. This conduces to a compromise solution between RS installation and cluster size, in order to maximize capacity, as well as performance.

Optimal choice between even- and uneven-aged forestry: the case of non-industrial private forest owners

An infinite-horizon discrete time model with multiple size-class structures using a transition matrix is built to assess optimal harvesting schedules in the context of Non-Industrial Private Forest (NIPF) owners. Three model specifications accounting for forest income, financial return on an asset and amenity valuations are considered. Numerical simulations suggest uneven-aged forest management where a rational forest owner adapts her or his forest policy by influencing the regeneration of trees or adjusting consumption dynamics depending on subjective time preference and market return rate dynamics on the financial asset. Moreover she or he does not value significantly non-market benefits captured by amenity valuations relatively to forest income.

How reliable is the monitoring of permanent vegetation plots? A test with multiple observers

Questions: A multiple plot design was developed for permanent vegetation plots. How reliable are the different methods used in this design and which changes can we measure? Location: Alpine meadows (2430 m a.s.l.) in the Swiss Alps. Methods: Four inventories were obtained from 40 m(2) plots: four subplots (0.4 m(2)) with a list of species, two 10m transects with the point method (50 points on each), one subplot (4 m2) with a list of species and visual cover estimates as a percentage and the complete plot (40 m(2)) with a list of species and visual estimates in classes. This design was tested by five to seven experienced botanists in three plots. Results: Whatever the sampling size, only 45-63% of the species were seen by all the observers. However, the majority of the overlooked species had cover < 0.1%. Pairs of observers overlooked 10-20% less species than single observers. The point method was the best method for cover estimate, but it took much longer than visual cover estimates, and 100 points allowed for the monitoring of only a very limited number of species. The visual estimate as a percentage was more precise than classes. Working in pairs did not improve the estimates, but one botanist repeating the survey is more reliable than a succession of different observers. Conclusion: Lists of species are insufficient for monitoring. It is necessary to add cover estimates to allow for subsequent interpretations in spite of the overlooked species. The choice of the method depends on the available resources: the point method is time consuming but gives precise data for a limited number of species, while visual estimates are quick but allow for recording only large changes in cover. Constant pairs of observers improve the reliability of the records.

Multiple paternity and its consequences in the white campion " Silene latifolia "

Summary Several studies have demonstrated that the number of pollen donors siring seeds of individual fruits is frequently greater than one and, consequently, that plants have multiple mates. Multiple paternity can have important consequences at the population level. It influences the genetic variability of a population, the reproductive success of males and the fitness of females and future generations. It also influences male-male interactions for fertilization and it is fundamental in providing opportunity of female choice. I investigated the occurrence and the importance of multiple paternity within fruits in natural populations of the dioecious Silene latifolia using microsatellite DNA markers, especially developed for this study. I found that multiple paternity occurs in all populations investigated in the European range of the species, varying from one to nine sires per fruit with a mean of three, suggesting that multiple paternity is highly prevalent in natural populations. In the presence of multiple paternity I investigated if there was a female genotype influence on siring success of the males. I used the same pollen mixture from two males and applied it to three replicate females of different relatedness (two full sisters and one unrelated). I found female genotype influence in one of the two populations investigated, which might reflect different population history. Since these results suggested some degree of female choice, we investigated whether the occurrence of multiple paternity and post-pollination selection could provide opportunity for inbreeding avoidance. First, I measured inbreeding depression at different life-cycle stages for offspring obtained by single-donor crosses with brothers or unrelated males replicated on distinct flowers on the same female plant. To address inbreeding avoidance, I determined paternity in crosses using mixed pollen loads of the two males. I found significant inbreeding depression in the studied population, even under benign experimental conditions, and although the unrelated male did not sire significantly more offspring, there was an effect of genetic dissimilarity on paternity. This suggests that paternity is affected by relatedness among mates, but maybe additionally affected by other factors such as pollen competitive ability or male-female interactions. Using inbred and outbred crosses, I further investigated sex ratio bias inheritance in this species, and found that sex ratio bias of the parental generation was significantly correlated to pollen germination success of the F2 generation, which suggests that sex ratio bias in this species results from the specific X/Y combination and not only on Y performance. An effect of X and Y is consistent with sex chromosome meiotic drive. In conclusion, I found multiple paternity to be widespread in the study species and that females of similar genotype produce similar paternity shares. I found that inbreeding depression is substantial, therefore receiving pollen from several donors might lead to fewer inbred offspring, I also found an effect of genetic dissimilarity on paternity shares, which indicates that there is some ability to discriminate against related pollen, although this seems not to be the only determinant of paternity outcome. Finally I found sex ratio bias to be dependent on both X and Y chromosomes as predicted by sex chromosome meiotic drive. Résumé Plusieurs études ont démontré qu'il n'était pas rare que les graines contenues dans un même fruit soient issues de la fécondation par plusieurs pollens provenant de mâles différents, ce qui sous-entend que les plantes peuvent avoir plusieurs partenaires sexuels. La paternité multiple peut avoir d'importantes conséquences au niveau populationnel dans la mesure où elle peut influencer le degré de variabilité génétique de la population, le succès reproducteur des mâles, la fitness des femelles et des futures générations. La paternité multiple peut également avoir un impact sur les interactions mâle-mâle lors de la fertilisation et peut être considérée comme fondamentale vis-à-vis de la femelle, qui y trouve alors une opportunité de choisir son ou ses partenaires. Dans le cadre de ce travail de thèse j'ai cherché à déterminer si la paternité multiple était un phénomène observable et important dans les populations naturelles de l'espèce dioïque, Silene latifolia. Pour ce faire, j'ai utilisé des marqueurs microsatellites, spécialement développés pour cette étude. J'ai observé des phénomènes de paternité multiple dans toutes les populations de l'étude, réparties dans l'aire de distribution européenne de l'espèce. Le nombre de pères par fruit varie de un à neuf, avec un nombre moyen de trois, ce qui signifie que la paternité multiple est très répandue dans les populations naturelles. En raison de ces résultats, je me suis demandée si le génotype de la femelle influence le succès de paternité des mâles. J'ai alors réalisé des pollinisations manuelles sur la base d'un mélange de pollens issus de deux mâles, que j'ai appliqué sur trois femelles (réplicats) présentant différents degrés d'apparentement (deux soeurs. et une femelle étrangère). Il ressort de cette expérience que le génotype de la femelle peut influencer la paternité dans l'une des deux populations étudiées, ce qui pourrait refléter des différences en terme d'histoire des populations. Dans la mesure où ces résultats suggèrent un certain degré de choix chez la femelle, j'ai cherché à savoir si la paternité multiple et la sélection post-pollinisation pouvaient être des moyens d'éviter les croisements consanguins. Dans un premier temps, j'ai évalué la dépression de consanguinité à différentes étapes du cycle de vie chez des descendants issus de croisements à un seul donneur, celui-ci étant alternativement un frère ou un étranger, répliqués sur plusieurs fleurs d'une même plante femelle. Afin d'estimer l'évitement de croisements consanguins, j'ai effectué des croisements dont le pollen était un mélange des deux mâles (frère et étranger), puis j'ai déterminé la paternité dans les fruits obtenus. J'ai pu mettre en évidence un effet de dépression de consanguinité- significatif dans les populations étudiées, même dans des conditions expérimentales moins rudes qu'à l'extérieur. Bien que le mâle étranger n'ait pas engendré un nombre significativement plus important de graines, il y avait un effet de dissimilarité génétique sur la paternité. Ceci suggère que la paternité est affectée par le degré d'apparentement entre les partenaires, mais qu'elle peut aussi être affectée par d'autres facteurs tels que la compétitivité du pollen ou encore par les interactions mâles-femelles. L'utilisation de croisements consanguins et hybrides m'a également permis d'étudier l'héritabilité du biais de sex ratio chez cette espèce. Il s'est avéré que le biais de sex ratio de la génération parentale était significativement corrélé au succès de germination du pollen de la génération F2, ce qui signifie que, chez cette espèce, le biais de sex ratio résulte d'une combinaison spécifique de X/Y et non uniquement de la performance de Y. Un effet de X et Y est compatible avec l'hypothèse de distorsion de ségrégation méiotique des chromosomes sexuels. En conclusion, il ressort de mes résultats que la paternité multiple est un phénomène largement répandu chez S. latifolia et la paternité accomplie par un mâle est plus similaire entre soeurs qu'avec une femelle étrangère J'ai également mis en évidence que la dépression de consanguinité a un impact considérable; aussi, recevoir du pollen de plusieurs donneurs différents pourrait permettre à la femelle de produire moins de descendants consanguins. J'ai aussi trouvé un effet de la dissimilarité génétique sur le partage de paternité, ce qui indique que la discrimination contre le pollen d'apparentés est possible, bien que cela ne semble pas être le seul facteur déterminant dans le résultat de la paternité. Enfin, j'ai trouvé que le biais de sex ratio est dépendant des deux chromosomes X et Y, conformément à la théorie de distorsion de ségrégation méiotique des chromosomes sexuels.

Why do females mate with multiple males ? The sexually selected sperm hypothesis

One debated issues in evolutionary biology is, why in many species females mate with multiple males. Several hypotheses have been put forward, yet the benefits of multiple mating (here defined as mating with several males) remain unclear in many cases. The sperm sexual selection (SSS) hypothesis has been developed to account for the widespread occurrence of multiple mating in females. It argues that multiple mating by females may rapidly spread, when initially a small fraction of the females mate multiply, and if there is a heritable difference among males in one or several of the four characteristics: (1) the quantity of sperm they produce; (2) the success of their sperm in reaching and fertilizing an egg; (3) their ability to displace the sperm that females stored during previous mating; and (4) their ability to prevent any other male from subsequently introducing sperm (e.g., differential efficiency of mating plugs).

Immunological mechanism of action and clinical profile of disease-modifying treatments in multiple sclerosis.

Multiple sclerosis (MS) is a life-long, potentially debilitating disease of the central nervous system (CNS). MS is considered to be an immune-mediated disease, and the presence of autoreactive peripheral lymphocytes in CNS compartments is believed to be critical in the process of demyelination and tissue damage in MS. Although MS is not currently a curable disease, several disease-modifying therapies (DMTs) are now available, or are in development. These DMTs are all thought to primarily suppress autoimmune activity within the CNS. Each therapy has its own mechanism of action (MoA) and, as a consequence, each has a different efficacy and safety profile. Neurologists can now select therapies on a more individual, patient-tailored basis, with the aim of maximizing potential for long-term efficacy without interruptions in treatment. The MoA and clinical profile of MS therapies are important considerations when making that choice or when switching therapies due to suboptimal disease response. This article therefore reviews the known and putative immunological MoAs alongside a summary of the clinical profile of therapies approved for relapsing forms of MS, and those in late-stage development, based on published data from pivotal randomized, controlled trials.

Cognition, mood and fatigue in patients in the early stage of multiple sclerosis.

QUESTION UNDER STUDY: Cognitive impairment occurs during multiple sclerosis (MS) and contributes to the burden of the disease, but its effect in the initial phase of MS still needs to be better understood. METHODS: We prospectively studied 127 early MS patients presenting with a clinically isolated syndrome (CIS) or definite MS, a mean disease duration of 2.6 years, and with minor disability (mean Expanded Disability Status Scale score 1.8). Patients were tested for long-term memory, executive functions, attention, fatigue, mood disorders, functional handicap and quality of life (QoL). Twenty-one CIS patients were excluded from study as the diagnosis of MS could not be confirmed. RESULTS: Over the 106 MS patients analysed, 31 (29.3%) were cognitively impaired (23.6% for memory, 10.4% for attention and 5.7% for executive functions). Cognitive deficits were already present in CIS patients in whom the diagnosis was not yet confirmed (20%). Impaired cognition was associated with anxiety (p = 0.05), depression(p = 0.004), fatigue (p = 0.03), handicap (p <0.001) and a lower QoL (p <0.001). After adjustment for QoL, handicap, depression, anxiety and fatigue were no longer associated with the presence of cognitive deficits. CONCLUSIONS: In this well-defined early MS group one third of the patients already exhibited cognitive deficits, which were usually apparent in an effortful learning situation and were generally mild. Mood disorders, fatigue, handicap and decreased QoL were all associated with the occurrence of cognitive deficits. QoL itself appeared to take all the other factors into account. Our results confirm the existence of an interplay between cognitive, affective and functional changes and fatigue in early MS.

Attractive silences in cricket courtship song : mate choice using a short-range signal /

Matings systems using signals for sexual communication have been studied extensively and results commonly suggest that females use these signals for locating males, species-identification, and mate choice. Although numerous mating systems employ multiple signals, research has generally focused on long-range signals perhaps due to their prominence and ease of study. This study focused on the short-range acoustic courtship song of crickets. The results presented here suggest this signal is under selection by female choice. Females mated preferentially with males having shorter silences between the two types of ticks within the song. The length of these silences (Gap 1) was correlated with male condition such that males having long silences were significantly lower in mass with respect to body size when compared to males having short silences. Both Gap 1 length and male condition were significantly repeatable within males over time suggesting the possibility these traits have a genetic basis. This study is the first empirical study to test female preferences within the natural variation of the courtship song. It now appears, at least in crickets, that both the longand short-range signals of a multi-signal mating system may contribute to male mating success.

Heritability of multiple mating by female field crickets, Gryllus integer (Orthoptera: Gryllidae)

The heritability of multiple mating in female Gryllus integer crickets was studied. Two preliminary experiments were conducted to determine when females first mate following the post-imaginal moult and to ascertain whether constant exposure to males affects female mating rate. Female Q. integer first mated at an average age of 3.6 days (S.D. = 2.3, Range = 0-8 days) . Exposing female crickets to courting males 24 hr daily did not significantly alter mating rates from those females in contact with males for only 5 hr per day. A heritability value of 0.690 ± 0.283 was calculated for multiple mating behavior in female Q. integer using a parent-offspring regression approach. Parental females mated between land 30 times (x 9.8, S . D. = 6. 6 ) and offspring matings ranged from 0 to 26 times (x 7 .3, S.D. = 3.4). Multiple mating is probably a sexually selected trait which functions as a mechanism of female choice and increases reproductive success through increased offspring production. Classical theory suggests that traits intimately related with fitness should exhibit negligible heritable variation. However, this study has shown that multiple mating, a trait closely linked with reproductive fitness, exhibits substantial heritability. These results are in concordance with a growing body of empirical evidence suggesting many fitness traits in natural populations demonstrate heritabilities far removed from zero. Various mechanisms which may maintain heritable variation for female multiple mating in wild, outbred Q. integer populations are discussed.

School choice behaviour of independent school parents

One hundred and thirty-three parents of students new ~o ~ive independent schools in Ontario wer. surveyed to inve~tigate school choice behaviour. Paren~s were asKed to indicate their reasons for changing schooling, ~he criteria for selection o~ a school and the nature of the search process. Parents were also asKed to ranK speci~ic precipitants for change and criteria for choice. Spearman RanK Correla.tion tests were run comparing precipitants for change and criteria for choice for the entire sample and sub-groups based on socioeconomic status, gender of the child and family size. No signl~icant differences were found between the various $ub-groups, however, there was a strong positive correlation between precipitants for change and criteria for choice.Chi sq,uare tests were run compa.ring the number of information sources utilized in the search process, and a comparison was made between the importance of the va.rious sources of information. The majority of parents were classified as ac~ive searchers, researching one alternative more carefully than others. Socioeconomic status was the only factor to have a sign ific:ant- effect on the ranKing of information sources.

Beyond g : putting multiple intelligences theory to the test /

The purpose of this study was to investigate Howard Gardner's (1983) Multiple Intelligences theory, which proposes that there are eight independent intelligences: Linguistic, Spatial, Logical/Mathematical, Interpersonal, Intrapersonal, Naturalistic, Bodily-Kinesthetic, and Musical. To explore Gardner's theory, two measures of each ability area were administered to 200 participants. Each participant also completed a measure of general cognitive ability, a personality inventory, an ability self-rating scale, and an ability self-report questionnaire. Nonverbal measures were included for most intelligence domains, and a wide range of content was sampled in Gardner's domains. Results showed that all tests of purely cognitive abilities were significantly correlated with the measure of general cognitive ability, whereas Musical, Bodily-Kinesthetic, and one of the Intrapersonal measures were not. Contrary to what Multiple Intelligences theory would seem to predict, correlations among the tests revealed a positive manifold and factor analysis indicated a large factor of general intelligence, with a mathematical reasoning test and a classification task from the Naturalistic domain having the highest ^- loadings. There were only minor sex differences in performance on the ability tests. Participants' self-estimates of ability were significantly and positively correlated with actual performance in some, but not all, intelligences. With regard to personality, a hypothesized association between Openness to Experience and crystallized intelligence was supported. The implications of the findings in regards to the nature of mental abilities were discussed, and recommendations for further research were made.

Aspects of spatial and habitat ecology of multiple Anopheles species (Diptera: Culicidae): malaria vectors in the highlands and foothills of Ecuador

The resurgence of malaria in highland regions of Africa, Oceania and recently in South America underlines the importance of the study of the ecology of highland mosquito vectors of malaria. Since the incidence of malaria is limited by the distribution of its vectors, the purpose of this PhD thesis was to examine aspects of the ecology of Anopheles mosquitoes in the Andes of Ecuador, South America. A historical literature and archival data review (Chapter 2) indicated that Anopheles pseudopunctipennis transmitted malaria in highland valleys of Ecuador prior to 1950, although it was eliminated through habitat removal and the use of chemical insecticides. Other anopheline species were previously limited to low-altitude regions, except in a few unconfirmed cases. A thorough larval collection effort (n=438 attempted collection sites) in all road-accessible parts of Ecuador except for the lowland Amazon basin was undertaken between 2008 - 2010 (Chapter 3). Larvae were identified morphologically and using molecular techniques (mitochondrial COl gene), and distribution maps indicated that all five species collected (Anopheles albimanus, An. pseudopunctipennis, Anopheles punctimacula, Anopheles oswaldoi s.l. and Anopheles eiseni) were more widespread throughout highland regions than previously recorded during the 1940s, with higher maximum altitudes for all except An. pseudopunctipennis (1541 m, 1930 m, 1906 m, 1233 m and 1873 m, respectively). During larval collections, to characterize species-specific larval habitat, a variety of abiotic and biotic habitat parameters were measured and compared between species-present and species-absent sites using chi-square tests and stepwise binary logistic regression analyses (Chapter 4). An. albimanus was significantly associated with permanent pools with sand substrates and An. pseudopunctipennis with gravel and boulder substrates. Both species were significantly associated with floating cyanobacterial mats and warmer temperatures, which may limit their presence in cooler highland regions. Anopheles punctimacula was collected more often than expected from algae-free, shaded pools with higher-than-average calculated dissolved oxygen. Anopheles oswaldoi s.l., the species occurring on the Amazonian side of the Andes, was associated with permanent, anthropogenic habitats such as roadside ditches and ponds. To address the hypothesis that human land use change is responsible for the emergence of multiple highland Anopheles species by creating larval habitat, common land uses in the western Andes were surveyed for standing water and potential larval habitat suitability (Chapter 5). Rivers and road edges provided large amounts of potentially suitable anopheline habitat in the western Andes, while cattle pasture also created potentially suitable habitat in irrigation canals and watering ponds. Other common land uses surveyed (banana farms, sugarcane plantations, mixed tree plantations, and empty lots) were usually established on steep slopes and had very little standing water present. Using distribution and larval habitat data, a GIS-based larval habitat distribution model for the common western species was constructed in ArcGIS v.l 0 (ESRI 2010) using derived data layers from field measurements and other sources (Chapter 6). The additive model predicted 76.4 - 97.9% of the field-observed collection localities of An. albimanus, An. pseudopunctipennis and An. punctimacula, although it could not accurately distinguish between species-absent and speciespresent sites due to its coarse scale. The model predicted distributional expansion and/or shift of one or more anopheline species into the following highland valleys with climate warming: Mira/Chota, Imbabura province, Tumbaco, Pichincha province, Pallatanga and Sibambe, Chimborazo province, and Yungilla, Azuay province. These valleys may serve as targeted sites of future monitoring to prevent highland epidemics of malaria. The human perceptions of malaria and mosquitoes in relation to land management practices were assessed through an interview-based survey (n=262) in both highlands and lowlands, of male and female land owners and managers of five property types (Chapter 7). Although respondents had a strong understanding of where the disease occurs in their own country and of the basic relationship among standing water, mosquitoes and malaria, about half of respondents in potential risk areas denied the current possibility of malaria infection on their own property. As well, about half of respondents with potential anopheline larval habitat did not report its presence, likely due to a highly specific definition of suitable mosquito habitat. Most respondents who are considered at risk of malaria currently use at least one type of mosquito bite prevention, most commonly bed nets. In conclusion, this interdisciplinary thesis examines the occurrence of Anopheles species in the lowland transition area and highlands in Ecuador, from a historic, geographic, ecological and sociological perspective.

Computation and Analysis of Multiple Structural-Change Models

In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order O(T 2) for any number of breaks. Our method can be applied to both pure and partial structural-change models. Secondly, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. We present simulation results pertaining to the behavior of the estimators and tests in finite samples. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program available upon request for non-profit academic use.