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

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.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

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.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz`s Bayesian information criterion and Hannan-Quinn criterion.

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.

On estimation and influence diagnostics for the Grubbs` model under heavy-tailed distributions

The Grubbs` measurement model is frequently used to compare several measuring devices. It is common to assume that the random terms have a normal distribution. However, such assumption makes the inference vulnerable to outlying observations, whereas scale mixtures of normal distributions have been an interesting alternative to produce robust estimates, keeping the elegancy and simplicity of the maximum likelihood theory. The aim of this paper is to develop an EM-type algorithm for the parameter estimation, and to use the local influence method to assess the robustness aspects of these parameter estimates under some usual perturbation schemes, In order to identify outliers and to criticize the model building we use the local influence procedure in a Study to compare the precision of several thermocouples. (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.

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.