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.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

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.

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

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.

Phylogenetic relationships and infrageneric classification of Epidendrum subgenus Amphiglottium (Laeliinae, Orchidaceae)

Epidendrum L. is the largest genus of Orchidaceae in the Neotropical region; it has an impressive morphological diversification, which imposes difficulties in delimitation of both infrageneric and interspecific boundaries. In this study, we review infrageneric boundaries within the subgenus Amphiglottium and try to contribute to the understanding of morphological diversification and taxa delimitation within this group. We tested the monophyly of the subgenus Amphiglottium sect. Amphiglottium, expanding previous phylogenetic investigations and reevaluated previous infrageneric classifications proposed. Sequence data from the trnL-trnF region were analyzed with both parsimony and maximum likelihood criteria. AFLP markers were also obtained and analyzed with phylogenetic and principal coordinate analyses. Additionally, we obtained chromosome numbers for representative species within the group. The results strengthen the monophyly of the subgenus Amphiglottium but do not support the current classification system proposed by previous authors. Only section Tuberculata comprises a well-supported monophyletic group, with sections Carinata and Integra not supported. Instead of morphology, biogeographical and ecological patterns are reflected in the phylogenetic signal in this group. This study also confirms the large variability of chromosome numbers for the subgenus Amphiglottium (numbers ranging from 2n = 24 to 2n = 240), suggesting that polyploidy and hybridization are probably important mechanisms of speciation within the group.

Relation of pretreatment sequence diversity in NS5A region of HCV genotype 1 with immune response between pegylated-INF/ribavirin therapy outcomes

Hepatitis C virus (HCV) infection frequently persists despite substantial virus-specific immune responses and the combination of pegylated interferon (INF)-alpha and ribavirin therapy. Major histocompatibility complex class I restricted CD8+ T cells are responsible for the control of viraemia in HCV infection, and several studies suggest protection against viral infection associated with specific HLAs. The reason for low rates of sustained viral response (SVR) in HCV patients remains unknown. Escape mutations in response to cytotoxic T lymphocyte are widely described; however, its influence in the treatment outcome is ill understood. Here, we investigate the differences in CD8 epitopes frequencies from the Los Alamos database between groups of patients that showed distinct response to pegylated alpha-INF with ribavirin therapy and test evidence of natural selection on the virus in those who failed treatment, using five maximum likelihood evolutionary models from PAML package. The group of sustained virological responders showed three epitopes with frequencies higher than Non-responders group, all had statistical support, and we observed evidence of selection pressure in the last group. No escape mutation was observed. Interestingly, the epitope VLSDFKTWL was 100% conserved in SVR group. These results suggest that the response to treatment can be explained by the increase in immune pressure, induced by interferon therapy, and the presence of those epitopes may represent an important factor in determining the outcome of therapy.

The genus Coleodactylus (Sphaerodactylinae, Gekkota) revisited: A molecular phylogenetic perspective

Nucleotide sequence data from a mitochondrial gene (16S) and two nuclear genes (c-mos, RAG-1) were used to evaluate the monophyly of the genus Coleodactylus, to provide the first phylogenetic hypothesis of relationships among its species in a cladistic framework, and to estimate the relative timing, of species divergences. Maximum Parsimony, Maximum Likelihood and Bayesian analyses of the combined data sets retrieved Coleodactylus as a monophyletic genus, although weakly Supported. Species were recovered as two genetically and morphological distinct clades, with C. amazonicus populations forming the sister taxon to the meridionalis group (C. brachystoma, C. meridionalis, C. natalensis, and C. septentrionalis). Within this group, C. septentrionalis was placed as the sister taxon to a clade comprising the rest of the species, C. meridionalis was recovered as the sister species to C. brachystoma, and C natalensis was found nested within C. meridionalis. Divergence time estimates based on penalized likelihood and Bayesian dating methods do not Support the previous hypothesis based on the Quaternary rain forest fragmentation model proposed to explain the diversification of the genus. The basal cladogenic event between major lineages of Coleodactylus was estimated to have occurred in the late Cretaceous (72.6 +/- 1.77 Mya), approximately at the same point in time than the other genera of Sphaerodactylinae diverged from each other. Within the meridionalis group, the split between C. septentrionalis and C. brachystoma + C. meridionalis was placed in the Eocene (46.4 +/- 4.22 Mya), and the divergence between C. brachystoma and C. meridionalis was estimated to have occurred in the Oligocene (29.3 +/- 4.33 Mya). Most intraspecific cladogenesis occurred through Miocene to Pliocene, and only for two conspecific samples and for C. natalensis could a Quaternary differentiation be assumed (1.9 +/- 1.3 Mya). (C) 2008 Elsevier Inc. All rights reserved.

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.

The genetic effects of Late Quaternary climatic changes over a tropical latitudinal gradient: diversification of an Atlantic Forest passerine

The increase in biodiversity from high to low latitudes is a widely recognized biogeographical pattern. According to the latitudinal gradient hypothesis (LGH), this pattern was shaped by differential effects of Late Quaternary climatic changes across a latitudinal gradient. Here, we evaluate the effects of climatic changes across a tropical latitudinal gradient and its implications to diversification of an Atlantic Forest (AF) endemic passerine. We studied the intraspecific diversification and historical demography of Sclerurus scansor, based on mitochondrial (ND2, ND3 and cytb) and nuclear (FIB7) gene sequences. Phylogenetic analyses recovered three well-supported clades associated with distinct latitudinal zones. Coalescent-based methods were applied to estimate divergence times and changes in effective population sizes. Estimates of divergence times indicate that intraspecific diversification took place during Middle-Late Pleistocene. Distinct demographic scenarios were identified, with the southern lineage exhibiting a clear signature of demographic expansion, while the central one remained more stable. The northern lineage, contrasting with LGH predictions, exhibited a clear sign of a recent bottleneck. Our results suggest that different AF regions reacted distinctly, even in opposite ways, under the same climatic period, producing simultaneously favourable scenarios for isolation and contact among populations.

Mitochondrial sequence data and Dipsacales phylogeny: Mixed models, partitioned Bayesian analyses, and model selection

Phylogenetic analyses of chloroplast DNA sequences, morphology, and combined data have provided consistent support for many of the major branches within the angiosperm, clade Dipsacales. Here we use sequences from three mitochondrial loci to test the existing broad scale phylogeny and in an attempt to resolve several relationships that have remained uncertain. Parsimony, maximum likelihood, and Bayesian analyses of a combined mitochondrial data set recover trees broadly consistent with previous studies, although resolution and support are lower than in the largest chloroplast analyses. Combining chloroplast and mitochondrial data results in a generally well-resolved and very strongly supported topology but the previously recognized problem areas remain. To investigate why these relationships have been difficult to resolve we conducted a series of experiments using different data partitions and heterogeneous substitution models. Usually more complex modeling schemes are favored regardless of the partitions recognized but model choice had little effect on topology or support values. In contrast there are consistent but weakly supported differences in the topologies recovered from coding and non-coding matrices. These conflicts directly correspond to relationships that were poorly resolved in analyses of the full combined chloroplast-mitochondrial data set. We suggest incongruent signal has contributed to our inability to confidently resolve these problem areas. (c) 2007 Elsevier Inc. All rights reserved.