Nonparametric estimation of Value-at-Risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

Statistics in archaeology: New directions

Connections between Statistics and Archaeology have always appeared veryfruitful. The objective of this paper is to offer an outlook of somestatistical techniques that are being developed in the most recentyears and that can be of interest for archaeologists in the short run.

The use of nonparametric contrasts in one-way layouts and random block designs

Nonparametric simple-contrast estimates for one-way layouts based on Hodges-Lehmann estimators for two samples and confidence intervals for all contrasts involving only two treatments are found in the literature.Tests for such contrasts are performed from the distribution of the maximum of the rank sum between two treatments. For random block designs, simple contrast estimates based on Hodges-Lehmann estimators for one sample are presented. However, discussions concerning the significance levels of more complex contrast tests in nonparametric statistics are not well outlined.This work aims at presenting a methodology to obtain p-values for any contrast types based on the construction of the permutations required by each design model using a C-language program for each design type. For small samples, all possible treatment configurations are performed in order to obtain the desired p-value. For large samples, a fixed number of random configurations are used. The program prompts the input of contrast coefficients, but does not assume the existence or orthogonality among them.In orthogonal contrasts, the decomposition of the value of the suitable statistic for each case is performed and it is observed that the same procedure used in the parametric analysis of variance can be applied in the nonparametric case, that is, each of the orthogonal contrasts has a chi(2) distribution with one degree of freedom. Also, the similarities between the p-values obtained for nonparametric contrasts and those obtained through approximations suggested in the literature are discussed.

Application of Local Rank Tests for Nonparametric Regression

Let Y_i = f(x_i) + E_i\ (1\le i\le n) with given covariates x_1\lt x_2\lt \cdots\lt x_n , an unknown regression function f and independent random errors E_i with median zero. It is shown how to apply several linear rank test statistics simultaneously in order to test monotonicity of f in various regions and to identify its local extrema.

Bayesian nonparametric latent variable models

L’un des problèmes importants en apprentissage automatique est de déterminer la complexité du modèle à apprendre. Une trop grande complexité mène au surapprentissage, ce qui correspond à trouver des structures qui n’existent pas réellement dans les données, tandis qu’une trop faible complexité mène au sous-apprentissage, c’est-à-dire que l’expressivité du modèle est insuffisante pour capturer l’ensemble des structures présentes dans les données. Pour certains modèles probabilistes, la complexité du modèle se traduit par l’introduction d’une ou plusieurs variables cachées dont le rôle est d’expliquer le processus génératif des données. Il existe diverses approches permettant d’identifier le nombre approprié de variables cachées d’un modèle. Cette thèse s’intéresse aux méthodes Bayésiennes nonparamétriques permettant de déterminer le nombre de variables cachées à utiliser ainsi que leur dimensionnalité. La popularisation des statistiques Bayésiennes nonparamétriques au sein de la communauté de l’apprentissage automatique est assez récente. Leur principal attrait vient du fait qu’elles offrent des modèles hautement flexibles et dont la complexité s’ajuste proportionnellement à la quantité de données disponibles. Au cours des dernières années, la recherche sur les méthodes d’apprentissage Bayésiennes nonparamétriques a porté sur trois aspects principaux : la construction de nouveaux modèles, le développement d’algorithmes d’inférence et les applications. Cette thèse présente nos contributions à ces trois sujets de recherches dans le contexte d’apprentissage de modèles à variables cachées. Dans un premier temps, nous introduisons le Pitman-Yor process mixture of Gaussians, un modèle permettant l’apprentissage de mélanges infinis de Gaussiennes. Nous présentons aussi un algorithme d’inférence permettant de découvrir les composantes cachées du modèle que nous évaluons sur deux applications concrètes de robotique. Nos résultats démontrent que l’approche proposée surpasse en performance et en flexibilité les approches classiques d’apprentissage. Dans un deuxième temps, nous proposons l’extended cascading Indian buffet process, un modèle servant de distribution de probabilité a priori sur l’espace des graphes dirigés acycliques. Dans le contexte de réseaux Bayésien, ce prior permet d’identifier à la fois la présence de variables cachées et la structure du réseau parmi celles-ci. Un algorithme d’inférence Monte Carlo par chaîne de Markov est utilisé pour l’évaluation sur des problèmes d’identification de structures et d’estimation de densités. Dans un dernier temps, nous proposons le Indian chefs process, un modèle plus général que l’extended cascading Indian buffet process servant à l’apprentissage de graphes et d’ordres. L’avantage du nouveau modèle est qu’il admet les connections entres les variables observables et qu’il prend en compte l’ordre des variables. Nous présentons un algorithme d’inférence Monte Carlo par chaîne de Markov avec saut réversible permettant l’apprentissage conjoint de graphes et d’ordres. L’évaluation est faite sur des problèmes d’estimations de densité et de test d’indépendance. Ce modèle est le premier modèle Bayésien nonparamétrique permettant d’apprendre des réseaux Bayésiens disposant d’une structure complètement arbitraire.

Estatística aplicada à química: dez dúvidas comuns

Ten common doubts of chemistry students and professionals about their statistical applications are discussed. The use of the N-1 denominator instead of N is described for the standard deviation. The statistical meaning of the denominators of the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV) are given for researchers using multivariate calibration methods. The reason why scientists and engineers use the average instead of the median is explained. Several problematic aspects about regression and correlation are treated. The popular use of triplicate experiments in teaching and research laboratories is seen to have its origin in statistical confidence intervals. Nonparametric statistics and bootstrapping methods round out the discussion.

Recalled and recorded bowel habits confirm early onset and high frequency of constipation in day-care nursery children

CONTEXT: Mothers recall early-onset constipation in children attending gastroenterology clinics. OBJECTIVES: To study the bowel habit of young children in the community to determine, first, whether early-onset constipation is confirmed in this setting and, second, the agreement between recalled and recorded bowel habit. METHODS:Defecation data of 57 children aged 6.0-40.7 mo were obtained by maternal recall (questionnaire on predominant stool characteristics) and by record (1,934 defecations registered prospectively at home and in the nursery). The bowel habit was classified according to stool frequency and proportion of stool characteristics (soft, hard and/or runny). Two criteria were used to classify recorded data, since the cutoff point for hard stools to identify constipation is undefined in children: predominant criterion and adult criterion, respectively with >50% and >25% of stools with altered consistency. Bowel habit categories were: adequate, constipation, functional diarrhea and "other bowel habit". Nonparametric statistics, and the Kappa index for agreement between recalled and recorded bowel habit, were used. RESULTS: Constipation occurred in 17.5%, 10.5%, 19.3% of the children by recall, the predominant and the adult criteria, respectively. Constipation was the main recalled alteration, vs 12.3% "other bowel habit". Only one child classified as having functional diarrhea (by the adult criterion). Agreement between recalled and recorded bowel habit was fair for constipation, by the predominant and the adult criteria (K = 0.28 and 0.24, respectively), but only slight (K <0.16) for other bowel habit categories. Individual data, however, pointed to a better relationship between recalled constipation and the adult rather than the predominant criterion. CONCLUSIONS: Frequent early-onset constipation was confirmed. Fair agreement between recalled and recorded constipation by the two used criteria indicates that recalled data are quite reliable to detect constipation.

Occupational therapists' use and perceptions of written client education materials

OBJECTIVE. The purpose of this study was to examine occupational therapists' use and perceptions of written education materials for clients and the factors that therapists consider before distributing written materials to clients This study also aimed to determine whether use and perceptions of these materials differed for older clients METHOD. A random sample of 50 occupational therapists from Queensland, Australia, working in adult physical disabilities settings was surveyed with a structured questionnaire Data were analyzed descriptively and with nonparametric statistics RESULTS. Of 49 participants who used written materials, 54% had given them to more than halt of their last 10 clients, regardless of the clients' age Written materials, most often information sheets developed by the participants themselves; handwritten notes; and pamphlets were principally used to reinforce verbal information. Clients' cognitive abilities, primary language, communication skills, vision, and level of education most often were considered before distributing written materials Although participants generally were positive about the content and effectiveness of materials, ratings were significantly less positive related to older clients CONCLUSION. Client education was a core treatment modality for participants in this study, with written media most commonly being used to supplement verbal education Because participants were least positive about the effectiveness of written materials for older clients, further development of materials for this audience may be indicated.

Acute aphasia after right hemisphere stroke

Abstract Right hemispheric stroke aphasia (RHSA) rarely occurs in right- or left-handed patients with their language representation in right hemisphere (RH). For right-handers, the term crossed aphasia is used. Single cases, multiple cases reports, and reviews suggest more variable anatomo-clinical correlations. We included retrospectively from our stroke data bank 16 patients (right- and left-handed, and ambidextrous) with aphasia after a single first-ever ischemic RH stroke. A control group was composed of 25 successive patients with left hemispheric stroke and aphasia (LHSA). For each patient, we analyzed four modalities of language (spontaneous fluency, naming, repetition, and comprehension) and recorded eventual impairment: (1) on admission (hyperacute) and (2) between day 3 and 14 (acute). Lesion volume and location as measured on computed tomography (CT) and magnetic resonance imaging (MRI) were transformed into Talairach stereotaxic space. Nonparametric statistics were used to compare impaired/nonimpaired patients. Comprehension and repetition were less frequently impaired after RHSA (respectively, 56% and 50%) than after LHSA (respectively, 84% and 80%, P = 0.05 and 0.04) only at hyperacute phase. Among RHSA, fewer left-handers/ambidextrous than right-handers had comprehension disorders at second evaluation (P = 0.013). Mean infarct size was similar in RHSA and LHSA with less posterior RHSA lesions (caudal to the posterior commissure). Comprehension and repetition impairments were more often associated with anterior lesions in RHSA (Fisher's exact test, P < 0.05). Despite the small size of the cohort, our findings suggest increased atypical anatomo-functional correlations of RH language representation, particularly in non-right-handed patients. Rapport de synthèse : Des aphasies secondaires à un accident vasculaire ischémique cérébral (AVC) hémisphérique droit sont rarement rencontrées chez des patients droitiers ou gauchers avec une représentation du langage dans l'hémisphère droit. Chez les droitiers, on parle d'aphasie croisée. Plusieurs études sur le sujet ont suggéré des corrélations anatomocliniques plus variables. Dans notre étude, nous avons inclus rétrospectivement, à partir d'une base de données de patients avec un AVC, seize patients (droitiers, gauchers et ambidextres) souffrant d'une aphasie suite à un premier et unique AVC ischémique hémisphérique droit. Un groupe contrôle est composé de vingt-cinq patients successifs avec une aphasie suite à un AVC ischémique hémisphérique gauche. Pour chaque patient, nous avons analysé quatre modalités de langage, à savoir la fluence spontanée, la dénomination, la répétition et la compréhension et leur éventuelle atteinte à deux moments distincts : 1) à l'admission (phase hyperaiguë) et 2) entre le 3e et le 14e jour (phase aiguë). Le volume et la localisation de la lésion mesurés, soit sur un CT-scanner soit sur une imagerie par résonance magnétique cérébrale, ont été analysés à l'aide de l'échelle stéréotaxique de Talairach. Des statistiques non paramétriques ont été utilisées pour comparer les patients atteints et non atteints. . La compréhension et la répétition étaient moins souvent atteintes, seulement en phase hyperaiguë, après une aphasie suite à un AVC hémisphérique droit (resp. 56% et 50%) plutôt que gauche (resp. 84 % et 80%, p= 0.05 et 0.04). Parmi les aphasies suite à un AVC ischémique hémisphérique droit, moins de gauchers et d'ambidextres que de droitiers avaient des troubles de la compréhension lors de la seconde évaluation (p=0.013}. La .taille moyenne de la zone infarcie était semblable entre les aphasies droites et gauches, avec moins de lésions postérieures (caudale à la commissure postérieure) lors des aphasies droites. Les troubles de la répétition et de la compréhension étaient plus souvent associés à des lésions antérieures lors d'aphasie droite. (Fischer's exact test, p>0.05). Malgré la petite taille de notre cohorte de patients, ces résultats suggèrent une augmentation des corrélations anatomocliniques atypiques lors d'une représentation du langage dans l'hémisphère droit, surtout chez les patients non droitiers.

Acute aphasia after right hemisphere stroke

Right hemispheric stroke aphasia (RHSA) rarely occurs in right- or left-handed patients with their language representation in right hemisphere (RH). For right-handers, the term crossed aphasia is used. Single cases, multiple cases reports, and reviews suggest more variable anatomo-clinical correlations. We included retrospectively from our stroke data bank 16 patients (right- and left-handed, and ambidextrous) with aphasia after a single first-ever ischemic RH stroke. A control group was composed of 25 successive patients with left hemispheric stroke and aphasia (LHSA). For each patient, we analyzed four modalities of language (spontaneous fluency, naming, repetition, and comprehension) and recorded eventual impairment: (1) on admission (hyperacute) and (2) between day 3 and 14 (acute). Lesion volume and location as measured on computed tomography (CT) and magnetic resonance imaging (MRI) were transformed into Talairach stereotaxic space. Nonparametric statistics were used to compare impaired/nonimpaired patients. Comprehension and repetition were less frequently impaired after RHSA (respectively, 56% and 50%) than after LHSA (respectively, 84% and 80%, P = 0.05 and 0.04) only at hyperacute phase. Among RHSA, fewer left-handers/ambidextrous than right-handers had comprehension disorders at second evaluation (P = 0.013). Mean infarct size was similar in RHSA and LHSA with less posterior RHSA lesions (caudal to the posterior commissure). Comprehension and repetition impairments were more often associated with anterior lesions in RHSA (Fisher's exact test, P < 0.05). Despite the small size of the cohort, our findings suggest increased atypical anatomo-functional correlations of RH language representation, particularly in non-right-handed patients.

Cómo aplicar las pruebas paramétricas bivariadas t de Student y ANOVA en SPSS.

Las pruebas paramétricas son un tipo de pruebas de significación estadística que cuantifican la asociación o independencia entre una variable cuantitativa y una categórica. Las pruebas paramétricas exigen ciertos requisitos previos para su aplicación: la distribución Normal de la variable cuantitativa en los grupos que se comparan, la homogeneidad de varianzas en las poblaciones de las que proceden los grupos y una n muestral no inferior a 30. Su incumplimiento conlleva la necesidad de recurrir a pruebas estadísticas no paramétricas. Las pruebas paramétricas se clasifican en dos: prueba t (para una muestra o para dos muestras relacionadas o independientes) y prueba ANOVA (para más de dos muestras independientes).

Assessing functional relations in single-case designs: Quantitative proposals in the context of the evidence-based movement

In the context of the evidence-based practices movement, the emphasis on computing effect sizes and combining them via meta-analysis does not preclude the demonstration of functional relations. For the latter aim, we propose to augment the visual analysis to add consistency to the decisions made on the existence of a functional relation without losing sight of the need for a methodological evaluation of what stimuli and reinforcement or punishment are used to control the behavior. Four options for quantification are reviewed, illustrated, and tested with simulated data. These quantifications include comparing the projected baseline with the actual treatment measurements, on the basis of either parametric or nonparametric statistics. The simulated data used to test the quantifications include nine data patterns in terms of the presence and type of effect and comprising ABAB and multiple baseline designs. Although none of the techniques is completely flawless in terms of detecting a functional relation only when it is present but not when it is absent, an option based on projecting split-middle trend and considering data variability as in exploratory data analysis proves to be the best performer for most data patterns. We suggest that the information on whether a functional relation has been demonstrated should be included in meta-analyses. It is also possible to use as a weight the inverse of the data variability measure used in the quantification for assessing the functional relation. We offer an easy to use code for open-source software for implementing some of the quantifications.

Estatística aplicada à química: dez dúvidas comuns

Ten common doubts of chemistry students and professionals about their statistical applications are discussed. The use of the N-1 denominator instead of N is described for the standard deviation. The statistical meaning of the denominators of the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV) are given for researchers using multivariate calibration methods. The reason why scientists and engineers use the average instead of the median is explained. Several problematic aspects about regression and correlation are treated. The popular use of triplicate experiments in teaching and research laboratories is seen to have its origin in statistical confidence intervals. Nonparametric statistics and bootstrapping methods round out the discussion.

Parámetros cuantitativos de la resonancia magnética cerebral en esclerosis múltiple y su correlación con la discapacidad

A pesar del amplio uso de la resonancia magnética en la esclerosis múltiple no se ha logrado una adecuada correlación clínico-imagenológica en esta enfermedad. Objetivo: Determinar la correlación del volumen normalizado de sustancia gris y del volumen de lesiones hipointensas en T1 obtenidos a partir de la resonancia magnética cerebral con la escala de discapacidad extendida en pacientes con diagnóstico de esclerosis múltiple. Materiales y métodos: Estudio retrospectivo en pacientes con diagnóstico de esclerosis múltiple de la Fundación Cardioinfantil. Se obtuvieron los resultados de la escala de discapacidad expandida así como análisis cuantitativo de las imágenes correspondientes de resonancia magnética por medio de la herramienta SIENA. Se cuantificaron el volumen del parénquima cerebral, sustancia gris, sustancia blanca y volumen de lesiones hipointensas en T1. Posteriormente, se relacionaron estos resultados con la escala de discapacidad extendida de Kurtzke previamente obtenida. Para el análisis estadístico se emplearon el test correlación de Spearman y t de Student y Hotelling. Resultados: Se incluyeron 58 pacientes, encontrándose correlaciones estadísticamente significativas entre la escala de discapacidad extendida y volumen de parénquima cerebral, volumen de sustancia gris y volumen de lesiones hipointensas en T1; de 0.384, 0.386 y 0.39. No se encontró una relación entre el volumen de sustancia blanca y la escala de discapacidad. Conclusiones: Existe una correlación clínico-imagenológica moderada en la esclerosis múltiple. La cuantificación de los parámetros propuestos en este estudio podría ser utilizada como herramienta en el seguimiento de la enfermedad y monitorización de nuevos tratamientos.