Papers by Klaus Vasconcellos
Http Dx Doi Org 10 1081 Sta 100104746, Aug 23, 2006
This paper discusses issues related to the improvement of maximum likelihood estimates in von Mis... more This paper discusses issues related to the improvement of maximum likelihood estimates in von Mises regression models. It obtains general matrix expressions for the secondorder biases of maximum likelihood estimates of the mean parameters and concentration parameters. The formulae are simple to compute, and give the biases by means of weighted linear regressions. Simulation results are presented assessing the performance of corrected maximum likelihood estimates in these models.
Bias and skewness in a general extreme-value regression model
Computational Statistics Data Analysis, Mar 1, 2011
ABSTRACT In this paper we introduce a general extreme-value regression model and derive Cox and S... more ABSTRACT In this paper we introduce a general extreme-value regression model and derive Cox and Snell’s (1968) general formulae for second-order biases of maximum likelihood estimates (MLEs) of the parameters. We obtain formulae which can be computed by means of weighted linear regressions. Furthermore, we give the skewness of order n^{−1/2} of the maximum likelihood estimators of the parameters by using Bowman and Shenton’s (1988) formula. A simulation study with results obtained with the use of Cox and Snell’s (1968) formulae is discussed. Practical uses of this model and of the derived formulae for bias correction are also presented.
We propose an analytical bias correction for the maximum likelihood estimators of the G o distrib... more We propose an analytical bias correction for the maximum likelihood estimators of the G o distribution. This distribution is a very powerful tool for speckled imagery analysis, since it is capable of describing a wide range of target roughness. We compare the performance of the corrected estimators with the corresponding original version using Monte Carlo simulation. This second-order bias correction leads to estimators which are better from both the bias and mean square error criteria.
Journal of Statistical Computation and Simulation, 2014
We consider the first-order Poisson autoregressive model proposed by McKenzie (1985) and Al-Osh a... more We consider the first-order Poisson autoregressive model proposed by McKenzie (1985) and Al-Osh and Alzaid (1987), which may be suitable in situations where the time series data is non-negative and integer valued. We derive the second order bias of the squared difference estimator (Weiß, 2012) for one of the parameters and show that this bias can be used to define a bias-reduced estimator. The behaviour of a modified conditional least squares estimator is also studied. Further, we access the asymptotic properties of the estimators here discussed. We present numerical evidence, based upon Monte Carlo simulation studies, showing that the here proposed bias-adjusted estimator outperforms the other estimators in small samples. We also present an application to a real data set.
Aspects of forecasting aggregate and discrete data
Brazilian Journal of Probability and Statistics, 2005
We propose a class of regression models where the response is beta distributed and the two parame... more We propose a class of regression models where the response is beta distributed and the two parameters that index the beta distribution are related to covariates and regression parameters. The proposed class of models is useful for modeling data that are restricted to the (0, 1) interval.
Estimators corrected for covariances among linear regressions
A Poisson INAR(1) process with a seasonal structure
Journal of Statistical Computation and Simulation, 2015
ABSTRACT This paper introduces a non-negative integer-valued autoregressive (INAR) process with s... more ABSTRACT This paper introduces a non-negative integer-valued autoregressive (INAR) process with seasonal structure of first order, which is an extension of the standard INAR(1) model proposed by Al-Osh and Alzaid [First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261-275]. The main properties of the model are derived such as its stationarity and autocorrelation function (ACF), among others. The conditional least squares and conditional maximum likelihood estimators of the model parameters are studied and their asymptotic properties are established. Some detailed discussion is dedicated to the case where the marginal distribution of the process is Poisson. A Monte Carlo experiment is conducted to evaluate and compare the performances of these estimators for finite sample sizes. The standard Yule-Walker approach is also considered for comparison purposes. The empirical results indicate that, in general, the conditional maximum likelihood estimator presents much better performance in terms of bias and mean square error. The model is illustrated using a real data set.
Brazilian Journal of Probability and Statistics, 2015
In this paper, we introduce a first order non-negative integer valued autoregressive process with... more In this paper, we introduce a first order non-negative integer valued autoregressive process with power series innovations based on the binomial thinning. This new model contains, as particular cases, several models such as the Poisson INAR model (Al-Osh and Alzaid (J. Time Series Anal. 8 (1987) 261-275)), the geometric INAR(1) model (Jazi, Jones and Lai (J. Iran. Stat. Soc. (JIRSS) 11 ) and many others. The main properties of the model are derived, such as mean, variance and the autocorrelation function. Yule-Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Special sub-models are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new model.
Brazilian Review of Econometrics, 1997
Neste artigo deduzimos fórmulas gerais para os vieses de segunda ordem dos estimadores de máxima ... more Neste artigo deduzimos fórmulas gerais para os vieses de segunda ordem dos estimadores de máxima verossimilhança dos parâmetros das médias e covariâncias dos modelos SUR ("Seemingly Unrelated R.egressions") nãcrlineares, modelos estes que apresentam correlação contemporânea entre os erros nas diferentes equações de um conjunto de equações de regressão. Tais vieses podem ser facilmente obtidos como vetores de estimadores de mínimos quadrados em regressões lineares ponderadas auxi liares. Eles são bastante simples de serem usados algebricamente para obter correções de viés em forma fechada nos casos especiais onde a inversa da matriz de informação tem forma fechada. O uso prático das correções é ilustrado por simulação, sugerindo que os estimadores corrigidos pelo viés são mais próximos dos parâmetros verdadeiros do que os estimadores clássicos de máxima verossimilhança) que são normalmente utilizados.
A Note on Inverse Moments of Binomial Variates
Brazilian review of …, 2000
Page 1. A Note on Inverse Moments of Binomial Variates Francisco Cribari-Neto' Nancy Lopes G... more Page 1. A Note on Inverse Moments of Binomial Variates Francisco Cribari-Neto' Nancy Lopes Garcia" Klaus LP Vasconcellos'" Abstract We show that the inverse moments of a binomial random variable are such that for all a E JR. ResuIno ...
Nearly Unbiased Maximum Likelihood Estimation for the Beta Distribution
Journal of Statistical Computation and Simulation, Oct 29, 2010
We analyze the finite-sample behavior of three second-order bias-corrected alternatives to the ma... more We analyze the finite-sample behavior of three second-order bias-corrected alternatives to the maximum likelihood estimator of the parameters that index the beta distribution. The three finite-sample corrections we consider are the conventional second-order bias corrected estimator (Cordeiro et al ., 1997), the alternative approach introduced by Firth (1993) and the bootstrap bias correction. We present numerical results comparing the performance of these estimators for thirty-six different values of the parameter vector. Our results reveal that analytical bias corrections considerably outperform numerical bias corrections obtained from bootstrapping schemes.
Computational Statistics Data Analysis, Oct 1, 2009
We propose a class of regression models where the observations are Dirichlet distributed and the ... more We propose a class of regression models where the observations are Dirichlet distributed and the parameters that index the Dirichlet distribution are related to covariates and unknown regression coefficients. The proposed class of models is useful for modeling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in . The rank of the matrix of unknown coefficients is estimated through a recently developed test statistics . Performance of rank estimators is assessed through Monte Carlo. Additionally, we apply Skovgaard's (Skovgaard, 2001) adjusted likelihood ratio statistic to test simple hypothesis in this new class of models. We show that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with high degree of accuracy. Some numerical results show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. Two empirical applications are presented and discussed.
Computational Statistics Data Analysis, Feb 1, 2007
We develop nearly unbiased estimators for the two-parameter Birnbaum-Saunders distribution [Birnb... more We develop nearly unbiased estimators for the two-parameter Birnbaum-Saunders distribution [Birnbaum, Z.W., Saunders, S.C., 1969a. A new family of life distributions. J. Appl. Probab. 6, 319-327], which is commonly used in reliability studies. We derive modified maximum likelihood estimators that are bias-free to second order. We also consider bootstrap-based bias correction. The numerical evidence we present favors three bias-adjusted estimators. Different interval estimation strategies are evaluated. Additionally, we derive a Bartlett correction that improves the finite-sample performance of the likelihood ratio test in finite samples.
SECOND-ORDER ASYMPTOTICS FOR SCORE TESTS IN HETEROSKEDASTIC t REGRESSION MODELS
Communications in Statistics Theory and Methods, Sep 2, 2006
This paper develops corrected score tests for heteroskedastic t regression models, thus generaliz... more This paper develops corrected score tests for heteroskedastic t regression models, thus generalizing results by Cordeiro, Ferrari and Paula[1] and Cribari-Neto and Ferrari[2] for normal regression models and by Ferrari and Arellano-Valle[3] for homoskedastic t regression models. We present, in matrix notation, Bartlett-type correction formulae to improve score tests in this class of models. The corrected score statistics have a
Http Dx Doi Org 10 1080 00949650412331270888, Aug 20, 2006
We discuss analytical bias corrections for maximum likelihood estimators in a regression model wh... more We discuss analytical bias corrections for maximum likelihood estimators in a regression model where the errors are Student-t distributed with unknown degrees of freedom. We propose a reparameterization of the number of degrees of freedom that produces a bias corrected estimator with very good small sample properties. This unknown number of degrees of freedom is assumed greater than 1, to guarantee a bounded likelihood function. We discuss some special cases of the general model and present some simulations which show that the corrected estimates perform better than their corresponding uncorrected versions in finite samples.
Dissertação submetida como requerimento parcial para obtenção do grau de Mestre em Estatística pe... more Dissertação submetida como requerimento parcial para obtenção do grau de Mestre em Estatística pela Universidade Federal de Pernambuco Recife, 16 de fevereiro de 2004 Dedico este trabalho a minha mãe, Martha Martínez, e a meu pai, Guillermo Ospina. A Yuri.
Estimadores corrigidos para covariâncias entre regressoes lineares
Revista De Matematica E Estatistica, 1998
Erratum: Erratum to Improved point and interval estimation for a beta regression model [Comput. Statist. Data Anal. 51 (2006) 960-981]
Computational Statistics Data Analysis, Jul 1, 2011
Computational Statistics Data Analysis, 2011
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Papers by Klaus Vasconcellos