Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Phylogeny of Thylamys (Didelphimorphia, Didelphidae) species, with special reference to Thylamys karimii

The genus Thylamys Gray, 1843 lives in the central and southern portions of South America inhabiting open and shrub-like vegetation, from prairies to dry forest habitats in contrast to the preference of other Didelphidae genera for more mesic environments. Thylamys is a speciose genus including T. elegans (Waterhouse, 1839), T. macrurus (Olfers, 1818), T. pallidior (Thomas, 1902), T. pusillus (Desmarest, 1804), T. venustus (Thomas, 1902), T. sponsorius (Thomas, 1921), T. cinderella (Thomas, 1902), T. tatei (Handley, 1957), T. karimii (Petter, 1968), and T. velutinus (Wagner, 1842) species. Previous phylogenetic analyses in this genus did not include the Brazilian species T. karimii, which is widely distributed in this country. In this study, phylogenetic analyses were performed to establish the relationships among the Brazilian T. karimii and all other previously analyzed species. We used 402-bp fragments of the mitochondrial cytochrome b gene, and the phylogeny estimates were conducted employing maximum parsimony (MP), maximum likelihood (ML), Bayesian (BY), and neighbor-joining (NJ). The topologies of the trees obtained in the different analyses were all similar and pointed out that T. karimii is the sister taxon of a group constituted of taxa from dry and arid environments named the dryland species. The dryland species consists of T. pusillus, T. pallidior, T. tatei, and T. elegans. The results of this work suggest five species groups in Thylamys. In one of them, T. velutinus and T. kariimi could constitute a sister group forming one Thylamys clade that colonized Brazil.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).

Heritability, determinants and reference values of renal length: a family-based population study.

OBJECTIVES: In this population-based study, reference values were generated for renal length, and the heritability and factors associated with kidney length were assessed. METHODS: Anthropometric parameters and renal ultrasound measurements were assessed in randomly selected nuclear families of European ancestry (Switzerland). The adjusted narrow sense heritability of kidney size parameters was estimated by maximum likelihood assuming multivariate normality after power transformation. Gender-specific reference centiles were generated for renal length according to body height in the subset of non-diabetic non-obese participants with normal renal function. RESULTS: We included 374 men and 419 women (mean ± SD, age 47 ± 18 and 48 ± 17 years, BMI 26.2 ± 4 and 24.5 ± 5 kg/m(2), respectively) from 205 families. Renal length was 11.4 ± 0.8 cm in men and 10.7 ± 0.8 cm in women; there was no difference between right and left renal length. Body height, weight and estimated glomerular filtration rate (eGFR) were positively associated with renal length, kidney function negatively, age quadratically, whereas gender and hypertension were not. The adjusted heritability estimates of renal length and volume were 47.3 ± 8.5 % and 45.5 ± 8.8 %, respectively (P < 0.001). CONCLUSION: The significant heritability of renal length and volume highlights the familial aggregation of this trait, independently of age and body size. Population-based references for renal length provide a useful guide for clinicians. KEY POINTS: • Renal length and volume are heritable traits, independent of age and size. • Based on a European population, gender-specific reference values/percentiles are provided for renal length. • Renal length correlates positively with body length and weight. • There was no difference between right and left renal lengths in this study. • This negates general teaching that the left kidney is larger and longer.

Oligocene CO2 decline promoted C4 photosynthesis in grasses.

C4 photosynthesis is an adaptation derived from the more common C3 photosynthetic pathway that confers a higher productivity under warm temperature and low atmospheric CO2 concentration [1, 2]. C4 evolution has been seen as a consequence of past atmospheric CO2 decline, such as the abrupt CO2 fall 32-25 million years ago (Mya) [3-6]. This relationship has never been tested rigorously, mainly because of a lack of accurate estimates of divergence times for the different C4 lineages [3]. In this study, we inferred a large phylogenetic tree for the grass family and estimated, through Bayesian molecular dating, the ages of the 17 to 18 independent grass C4 lineages. The first transition from C3 to C4 photosynthesis occurred in the Chloridoideae subfamily, 32.0-25.0 Mya. The link between CO2 decrease and transition to C4 photosynthesis was tested by a novel maximum likelihood approach. We showed that the model incorporating the atmospheric CO2 levels was significantly better than the null model, supporting the importance of CO2 decline on C4 photosynthesis evolvability. This finding is relevant for understanding the origin of C4 photosynthesis in grasses, which is one of the most successful ecological and evolutionary innovations in plant history.

Inter-informant agreement and prevalence estimates for substance use disorders: direct interview versus family history method.

OBJECTIVES: Family studies typically use multiple sources of information on each individual including direct interviews and family history information. The aims of the present study were to: (1) assess agreement for diagnoses of specific substance use disorders between direct interviews and the family history method; (2) compare prevalence estimates according to the two methods; (3) test strategies to approximate prevalence estimates according to family history reports to those based on direct interviews; (4) determine covariates of inter-informant agreement; and (5) identify covariates that affect the likelihood of reporting disorders by informants. METHODS: Analyses were based on family study data which included 1621 distinct informant (first-degree relatives and spouses) - index subject pairs. RESULTS: Our main findings were: (1) inter-informant agreement was fair to good for all substance disorders, except for alcohol abuse; (2) the family history method underestimated the prevalence of drug but not alcohol use disorders; (3) lowering diagnostic thresholds for drug disorders and combining multiple family histories increased the accuracy of prevalence estimates for these disorders according to the family history method; (4) female sex of index subjects was associated with higher agreement for nearly all disorders; and (5) informants who themselves had a history of the same substance use disorder were more likely to report this disorder in their relatives, which entails the risk of overestimation of the size of familial aggregation. CONCLUSION: Our findings have important implications for the best-estimate procedure applied in family studies.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Parent-child agreement and prevalence estimates of diagnoses in childhood: direct interview versus family history method.

Diagnostic information on children is typically elicited from both children and their parents. The aims of the present paper were to: (1) compare prevalence estimates according to maternal reports, paternal reports and direct interviews of children [major depressive disorder (MDD), anxiety and attention-deficit and disruptive behavioural disorders]; (2) assess mother-child, father-child and inter-parental agreement for these disorders; (3) determine the association between several child, parent and familial characteristics and the degree of diagnostic agreement or the likelihood of parental reporting; (4) determine the predictive validity of diagnostic information provided by parents and children. Analyses were based on 235 mother-offspring, 189 father-offspring and 128 mother-father pairs. Diagnostic assessment included the Kiddie-schedule for Affective Disorders and Schizophrenia (K-SADS) (offspring) and the Diagnostic Interview for Genetic Studies (DIGS) (parents and offspring at follow-up) interviews. Parental reports were collected using the Family History - Research Diagnostic Criteria (FH-RDC). Analyses revealed: (1) prevalence estimates for internalizing disorders were generally lower according to parental information than according to the K-SADS; (2) mother-child and father-child agreement was poor and within similar ranges; (3) parents with a history of MDD or attention deficit hyperactivity disorder (ADHD) reported these disorders in their children more frequently; (4) in a sub-sample followed-up into adulthood, diagnoses of MDD, separation anxiety and conduct disorder at baseline concurred with the corresponding lifetime diagnosis at age 19 according to the child rather than according to the parents. In conclusion, our findings support large discrepancies of diagnostic information provided by parents and children with generally lower reporting of internalizing disorders by parents, and differential reporting of depression and ADHD by parental disease status. Follow-up data also supports the validity of information provided by adolescent offspring.

Stochastic time-concentration activity models for cytotoxicity in 3D brain cell cultures.

BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

Heritability of renal function in hypertensive families of African descent in the Seychelles (Indian Ocean).

BACKGROUND: We estimated the heritability of three measures of glomerular filtration rate (GFR) in hypertensive families of African descent in the Seychelles (Indian Ocean). METHODS: Families with at least two hypertensive siblings and an average of two normotensive siblings were identified through a national hypertension register. Using the ASSOC program in SAGE (Statistical Analysis in Genetic Epidemiology), the age- and gender-adjusted narrow sense heritability of GFR was estimated by maximum likelihood assuming multivariate normality after power transformation. ASSOC can calculate the additive polygenic component of the variance of a trait from pedigree data in the presence of other familial correlations. The effects of body mass index (BMI), blood pressure, natriuresis, along with sodium to potassium ratio in urine and diabetes, were also tested as covariates. RESULTS: Inulin clearance, 24-hour creatinine clearance, and GFR based on the Cockcroft-Gault formula were available for 348 persons from 66 pedigrees. The age- and gender-adjusted correlations (+/- SE) were 0.51 (+/- 0.04) between inulin clearance and creatinine clearance, 0.53 (+/- 0.04) between inulin clearance and Cockcroft-Gault formula and 0.66 (+/- 0.03) between creatinine clearance and Cockcroft-Gault formula. The age- and gender-adjusted heritabilities (+/- SE) of GFR were 0.41 (+/- 0.10) for inulin clearance, 0.52 (+/- 0.13) for creatinine clearance, and 0.82 (+/- 0.09) for Cockcroft-Gault formula. Adjustment for BMI slightly lowered the correlations and heritabilities for all measurements whereas adjustment for blood pressure had virtually no effect. CONCLUSION: The significant heritability estimates of GFR in our sample of families of African descent confirm the familial aggregation of this trait and justify further analyses aimed at discovering genetic determinants of GFR.

Inter-informant agreement and prevalence estimates for mood syndromes: Direct interview vs. family history method.

BACKGROUND: The use of the family history method is recommended in family studies as a type of proxy interview of non-participating relatives. However, using different sources of information can result in bias as direct interviews may provide a higher likelihood of assigning diagnoses than family history reports. The aims of the present study were to: 1) compare diagnoses for threshold and subthreshold mood syndromes from interviews to those relying on information from relatives; 2) test the appropriateness of lowering the diagnostic threshold and combining multiple reports from the family history method to obtain comparable prevalence estimates to the interviews; 3) identify factors that influence the likelihood of agreement and reporting of disorders by informants. METHODS: Within a family study, 1621 informant-index subject pairs were identified. DSM-5 diagnoses from direct interviews of index subjects were compared to those derived from family history information provided by their first-degree relatives. RESULTS: 1) Inter-informant agreement was acceptable for Mania, but low for all other mood syndromes. 2) Except for Mania and subthreshold depression, the family history method provided significantly lower prevalence estimates. The gap improved for all other syndromes after lowering the threshold of the family history method. 3) Individuals who had a history of depression themselves were more likely to report depression in their relatives. LIMITATIONS: Low proportion of affected individuals for manic syndromes and lack of independence of data. CONCLUSIONS: The higher likelihood of reporting disorders by affected informants entails the risk of overestimation of the size of familial aggregation of depression.

High heritability of ambulatory blood pressure in families of East African descent.

We estimated the heritability of ambulatory systolic blood pressure (SBP), diastolic blood pressure (DBP), and pulse pressure (PP) in east African families with at least 2 hypertensive siblings and living in the Seychelles islands (Indian Ocean). The sample consisted of 314 individuals (147 men and 167 women), both normotensive and hypertensive, from 76 pedigrees (mean+/-SD of 4.1+/-2.8 persons per pedigree). After a 2-week off-treatment period, daytime and nighttime ambulatory blood pressure (BP) was monitored. Office BP was measured with a standard mercury sphygmomanometer. We estimated by maximum likelihood the age- and sex-adjusted heritabilities from the additive polygenic component of the variance of the traits allowing for the presence of other familial correlations. We also adjusted for ascertainment (ie, for the fact that 2 siblings had to be hypertensive) and examined the effect of adjusting for body mass index, 24-hour urinary excretion of sodium and potassium, plasma renin activity, and plasma aldosterone concentration. Heritability estimates (+/-SE) for ambulatory SBP, DBP, and PP were, respectively, 0.37+/-0.12/0.24+/-0.12/0.54+/-0.12 for daytime and 0.34+/-0.13/ 0.37+/-0.15/0.47+/-0.12 for nighttime measurements (P<0.05 for all estimates). Heritability estimates for office SBP, DBP, and PP were, respectively, 0.20+/-0.11, 0.05+/-0.09, and 0.37+/-0.12. Heritability estimates for SBP varied markedly according to whether participants were treated for hypertension at baseline. The present data show that ambulatory BP and PP have a high heritability in families of African descent. They also demonstrate that antihypertensive treatment and the number of BP measurements have a major influence on the heritability estimates.

Generation of Simulated Daily Precipitation and Air and Soil Temperatures, January 2000

This paper describes a maximum likelihood method using historical weather data to estimate a parametric model of daily precipitation and maximum and minimum air temperatures. Parameter estimates are reported for Brookings, SD, and Boone, IA, to illustrate the procedure. The use of this parametric model to generate stochastic time series of daily weather is then summarized. A soil temperature model is described that determines daily average, maximum, and minimum soil temperatures based on air temperatures and precipitation, following a lagged process due to soil heat storage and other factors.

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

It's still 2%: evidence on convergence from 116 years of the US States panel data

A new debate over the speed of convergence in per capita income across economies is going on. Cross sectional estimates support the idea of slow convergence of about two percent per year. Panel data estimates support the idea of fast convergence of five, ten or even twenty percent per year. This paper shows that, if you ``do it right'', even the panel data estimation method yields the result of slow convergence of about two percent per year.