Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil

This work is an assessment of frequency of extreme values (EVs) of daily rainfall in the city of Sao Paulo. Brazil, over the period 1933-2005, based on the peaks-over-threshold (POT) and Generalized Pareto Distribution (GPD) approach. Usually. a GPD model is fitted to a sample of POT Values Selected With a constant threshold. However. in this work we use time-dependent thresholds, composed of relatively large p quantities (for example p of 0.97) of daily rainfall amounts computed from all available data. Samples of POT values were extracted with several Values of p. Four different GPD models (GPD-1, GPD-2, GPD-3. and GDP-4) were fitted to each one of these samples by the maximum likelihood (ML) method. The shape parameter was assumed constant for the four models, but time-varying covariates were incorporated into scale parameter of GPD-2. GPD-3, and GPD-4, describing annual cycle in GPD-2. linear trend in GPD-3, and both annual cycle and linear trend in GPD-4. The GPD-1 with constant scale and shape parameters is the simplest model. For identification of the best model among the four models WC used rescaled Akaike Information Criterion (AIC) with second-order bias correction. This criterion isolates GPD-3 as the best model, i.e. the one with positive linear trend in the scale parameter. The slope of this trend is significant compared to the null hypothesis of no trend, for about 98% confidence level. The non-parametric Mann-Kendall test also showed presence of positive trend in the annual frequency of excess over high thresholds. with p-value being virtually zero. Therefore. there is strong evidence that high quantiles of daily rainfall in the city of Sao Paulo have been increasing in magnitude and frequency over time. For example. 0.99 quantiles of daily rainfall amount have increased by about 40 mm between 1933 and 2005. Copyright (C) 2008 Royal Meteorological Society

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

Bayesian analysis of skew-t multivariate null intercept measurement error model

The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001; J R Stat Soc, Ser B 65:367-389, 2003; Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.

Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

DIAGNOSTIC TECHNIQUES OF LOCAL INFLUENCE IN SPATIAL ANALYSIS OF SOYBEAN YIELD

Modeling of spatial dependence structure, concerning geoestatistics approach, is an indispensable tool for fixing parameters that define this structure, applied on interpolation of values in places that are not sampled, by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations on sampled data. Thus, this trial aimed at using diagnostics techniques of local influence in spatial linear Gaussians models, applied at geoestatistics in order to evaluate sensitivity of maximum likelihood estimators and restrict maximum likelihood to small perturbations in these data. So, studies with simulated and experimental data were performed. Those results, obtained from the study of real data, allowed us to conclude that the presence of atypical values among the sampled data can have a strong influence on thematic maps, changing, therefore, the spatial dependence. The application of diagnostics techniques of local influence should be part of any geoestatistic analysis, ensuring that the information from thematic maps has better quality and can be used with greater security by farmers.

Forest-obligate Sabethes mosquitoes suggest palaeoecological perturbations

The origin of tropical forest diversity has been hotly debated for decades. Although specific mechanisms vary, many such explanations propose some vicariance in the distribution of species during glacial cycles and several have been supported by genetic evidence in Neotropical taxa. However, no consensus exists with regard to the extent or time frame of the vicariance events. Here, we analyse the cytochrome oxidase II mitochondrial gene of 250 Sabethes albiprivus B mosquitoes sampled from western Sao Paulo in Brazil. There was very low population structuring among collection sites (Phi(ST) = 0.03, P = 0.04). Historic demographic analyses and the contemporary geographic distribution of genetic diversity suggest that the populations sampled are not at demographic equilibrium. Three distinct mitochondrial clades were observed in the samples, one of which differed significantly in its geographic distribution relative to the other two within a small sampling area (similar to 70 x 35 km). This fact, supported by the inability of maximum likelihood analyses to achieve adequate fits to simple models for the population demography of the species, suggests a more complex history, possibly involving disjunct forest refugia. This hypothesis is supported by a genetic signal of recent population growth, which is expected if population sizes of this forest-obligate insect increased during the forest expansions that followed glacial periods. Although a time frame cannot be reliably inferred for the vicariance event leading to the three genetic clades, molecular clock estimates place this at similar to 1 Myr before present.

Phylogenetic analysis of the Brazilian microendemic Paepalanthus subgenus Xeractis (Eriocaulaceae) inferred from morphology

Paepalanthus subgenus Xeractis (Eriocaulaceae) comprises 28 recognized species endemic to the Espinhaco Range, in Minas Gerais state, Brazil. Most species of the subgenus are restricted to small localities and critically endangered, but still in need of systematic study. The monophyly of the subgenus has already been tested, but only with a few species. Our study presents the first phylogenetic hypothesis within the group, based on morphology. A maximum parsimony analysis was conducted on a matrix of 30 characters for 30 terminal taxa, including all species of the subgenus and two outgroups. The biogeographical hypotheses for the subgenus were inferred based on dispersal-vicariance analysis (DIVA). The analysis provided one most-parsimonious hypothesis that supports most of the latest published subdivisions (sections and series). However, some conflicts remain concerning the position of a few species and the relationships between sections. The distribution and origin(s) of microendemism are also discussed, providing the ground for conservation strategies to be developed in the region. (C) 2011 The Linnean Society of London, Botanical Journal of the Linnean Society, 2011, 167, 137-152.

Copia Retrotransposon in the Zaprionus Genus: Another Case of Transposable Element Sharing with the Drosophila melanogaster Subgroup

Copia is a retrotransposon that appears to be distributed widely among the Drosophilidae subfamily. Evolutionary analyses of regulatory regions have indicated that the Copia retrotransposon evolved through both positive and purifying selection, and that horizontal transfer (HT) could also explain its patchy distribution of the among the subfamilies of the melanogaster subgroup. Additionally, Copia elements could also have transferred between melanogaster subgroup and other species of Drosophilidae-D. willistoni and Z. tuberculatus. In this study, we surveyed seven species of the Zaprionus genus by sequencing the LTR-ULR and reverse transcriptase regions, and by using RT-PCR in order to understand the distribution and evolutionary history of Copia in the Zaprionus genus. The Copia element was detected, and was transcriptionally active, in all species investigated. Structural and selection analysis revealed Zaprionus elements to be closely related to the most ancient subfamily of the melanogaster subgroup, and they seem to be evolving mainly under relaxed purifying selection. Taken together, these results allowed us to classify the Zaprionus sequences as a new subfamily-ZapCopia, a member of the Copia retrotransposon family of the melanogaster subgroup. These findings indicate that the Copia retrotransposon is an ancient component of the genomes of the Zaprionus species and broaden our understanding of the diversity of retrotransposons in the Zaprionus genus.

Structural Aspects of the Distinct Biochemical Properties of Glutaredoxin 1 and Glutaredoxin 2 from Saccharomyces cerevisiae

Glutaredoxins (Grxs) are small (9-12 kDa) heat-stable proteins that are ubiquitously distributed. In Saccharomyces cerevisiae, seven Grx enzymes have been identified. Two of them (yGrx1 and yGrx2) are dithiolic, possessing a conserved Cys-Pro-Tyr-Cys motif. Here, we show that yGrx2 has a specific activity 15 times higher than that of yGrx1, although these two oxidoreductases share 64% identity and 85% similarity with respect to their amino acid sequences. Further characterization of the enzymatic activities through two-substrate kinetics analysis revealed that yGrx2 possesses a lower Km for glutathione and a higher turnover than yGrx1. To better comprehend these biochemical differences, the pK(a) of the N-terminal active-site cysteines (Cys27) of these two proteins and of the yGrx2-C30S mutant were determined. Since the pK(a) values of the yGrx1 and yGix2 Cys27 residues are very similar, these parameters cannot account for the difference observed between their specific activities. Therefore, crystal structures of yGrx2 in the oxidized form and with a glutathionyl mixed disulfide were determined at resolutions of 2.05 and 1.91 angstrom, respectively. Comparisons of yGrx2 structures with the recently determined structures of yGrx1 provided insights into their remarkable functional divergence. We hypothesize that the substitutions of Ser23 and Gln52 in yGrx1 by Ala23 and Glu52 in yGrx2 modify the capability of the active-site C-terminal cysteine to attack the mixed disulfide between the N-terminal active-site cysteine and the glutathione molecule. Mutagenesis studies supported this hypothesis. The observed structural and functional differences between yGrx1 and yGrx2 may reflect variations in substrate specificity. (C) 2008 Elsevier Ltd. All rights reserved.

A Phylogenetic Lineage of Closely Related Trypanosomes (Trypanosomatidae, Kinetoplastida) of Anurans and Sand Flies (Psychodidae, Diptera) Sharing the Same Ecotopes in Brazilian Amazonia

Analysis of the phylogenetic relationships among trypanosomes from vertebrates and invertebrates disclosed a new lineage of trypanosomes circulating among anurans and sand flies that share the same ecotopes in Brazilian Amazonia. This assemblage of closely related trypanosomes was determined by comparing whole SSU rDNA sequences of anuran trypanosomes from the Brazilian biomes of Amazonia, the Pantanal, and the Atlantic Forest and from Europe, North America, and Africa, and from trypanosomes of sand flies from Amazonia. Phylogenetic trees based on maximum likelihood and parsimony corroborated the positioning of all new anuran trypanosomes in the aquatic clade but did not support the monophyly of anuran trypanosomes. However, all analyses always supported four major clades (An01-04) of anuran trypanosomes. Clade An04 is composed of trypanosomes from exotic anurans. Isolates in clades An01 and An02 were from Brazilian frogs and toads captured in the three biomes studied, Amazonia, the Pantanal and the Atlantic Forest. Clade An01 contains mostly isolates from Hylidae whereas clade An02 comprises mostly isolates from Bufonidae; and clade An03 contains trypanosomes from sand flies and anurans of Bufonidae, Leptodactylidae, and Leiuperidae exclusively from Amazonia. To our knowledge, this is the first study describing morphological and growth features, and molecular phylogenetic affiliation of trypanosomes from anurans and phlebotomines, incriminating these flies as invertebrate hosts and probably also as important vectors of Amazonian terrestrial anuran trypanosomes.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.