We evaluate the finite-sample behavior of different heteros-ke-das-ticity-consistent covariance matrix estimators, under both constant and unequal error variances. We consider the estimator proposed by Halbert White (HC0), and also its variants known as HC2, HC3, and HC4; the latter was recently proposed by Cribari-Neto ( 2004 Cribari-Neto , F. ( 2004 ). Asymptotic inference under heteroskedasticity of unknown form . Computat. Statist. Data Anal. 45 : 215 – 233 . [Crossref], [Web of Science ®] [Google Scholar] ). We propose a new covariance matrix estimator: HC5. It is the first consistent estimator to explicitly take into account the effect that the maximal leverage has on the associated inference. Our numerical results show that quasi-t inference based on HC5 is typically more reliable than inference based on other covariance matrix estimators.

In this paper, we consider the two-parameter Birnbaum–Saunders distribution proposed by Birnbaum and Saunders [Birnbaum, Z.W. and Saunders, S.C., 1969, A new family of life distributions. Journal of Applied Probability, 6, 319–327], which is commonly used for modeling the lifetime of materials and equipment. We consider different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the distribution via bootstrap (parametric and nonparametric). The numerical evidence favors a particular bootstrap estimator based on parametric resampling. Finally, an example with real data is presented and discussed.

This paper deals with numerical problems arising when performing maximum likelihood parameter estimation in speckled imagery using small samples. The noise that appears in images obtained with coherent illumination, as is the case of sonar, laser, ultrasound-B, and synthetic aperture radar, is called speckle, and it can neither be assumed Gaussian nor additive. The properties of speckle noise are well described by the multiplicative model, a statistical framework from which stem several important distributions. Amongst these distributions, one is regarded as the universal model for speckled data, namely, the law. This paper deals with amplitude data, so the distribution will be used. The literature reports that techniques for obtaining estimates (maximum likelihood, based on moments and on order statistics) of the parameters of the distribution require samples of hundreds, even thousands, of observations in order to obtain sensible values. This is verified for maximum likelihood estimation, and a proposal based on alternate optimization is made to alleviate this situation. The proposal is assessed with real and simulated data, showing that the convergence problems are no longer present. A Monte Carlo experiment is devised to estimate the quality of maximum likelihood estimators in small samples, and real data is successfully analyzed with the proposed alternated procedure. Stylized empirical influence functions are computed and used to choose a strategy for computing maximum likelihood estimates that is resistant to outliers.

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.