Is It Always Necessary to Take Sample Selection into Account?

We compare a simple ordinary least squares (OLS) with the maximum likelihood estimation of the Tobit I and Tobit II regression models, in the selected sample. We propose a new measure to quantify the performance of OLS.     

speed of covergence to the extreme value distributions on their probability ploting parers

The speed of convergence of the distribution of the normalized maximum, of a sample of independent and identically distributed random variables, to its asymptotic distribution is considered in this article. Assuming that the cumulative distribution function of the random variables is known, the error committed replacing the actual distribution of the normalized maximum by its asympotic distribution is studied. Instead of using the arithmetical scale of probabilities, we measure the difference between the actual and asympotic distribution in terms of the double-log scale used for building the probability plotting paper for the the latter. We demonstrate that the difference between the double-log values corresponding to two probabilities in the upper tail is almost exactly equal to the logarithm of the distribution may not be uniform in this double-log scale and that the difference between the actual and asymptotic distributions, on the probebility plotting paper, may be a logarithmic, power, or even exponential function in the upper tail when the latter distribution is of Fisher-Tippett type I, but that difference is at most logarithmic in the upper tail for type II and III distributions. This fact is exploited to obtain transformed variables that converge tothe asymptotic distribution faster than the original variable on the probabilites plotting paper     

On the Smoothness of Projections in Statistical Models

Here we examine the existence of the projection of a probability measure in a parametric statistical model. Once, in a general framework, the existence of the projection is established, we consider the problem from a statistical point of view, modeling a parametric statistical model as a convenient manifold.     

Prior Density Selection as a Particular Case of Bayesian Model Selection: A Predictive Approach

A Bayesian model consists of two elements: a sampling model and a prior density. The problem of selecting a prior density is nothing but the problem of selecting a Bayesian model where the sampling model is fixed. A predictive approach is used through a decision problem where the loss function is the squared L ² distance between the sampling density and the posterior predictive density, because the aim of the method is to choose the prior that provides a posterior predictive density as good as possible. An algorithm is developed for solving the problem; this algorithm is based on Lavine's linearization technique.     

A Goodness-of-Fit Test for the Gumbel Distribution Based on Kullback–Leibler Information

A goodness-of-fit test for the Gumbel distribution is proposed. This test is based on the Kullback–Leibler discrimination information methodology proposed by Song (2002 Song , K. S. ( 2002 ). Goodness-of-fit tests based on Kullback–Leibler discrimination information . IEEE Trans. Inform. Theor. 48 : 1103 – 1117 .[Crossref], [Web of Science ®] , [Google Scholar]). The critical values of the test were obtained by using Monte Carlo simulation for small sample sizes and different levels of significance. The proposed test is compared with the tests developed by Stephens (1977 Stephens , M. ( 1977 ). Goodness-of-fit tests for the extreme value distribution . Biometrika 65 : 730 – 737 . [Google Scholar]), Chandra et al. (1981 Chandra , M. , Singpurwalla , N. D. , Stephens , M. A. ( 1981 ). Kolmogorov statistics for tests of fit for the extreme value and Weibull distributions . J. Amer. Statist. Assoc. 74 : 729 – 735 . [Google Scholar]), and the test given by Kinnison (1989 Kinnison , R. (1989). Correlation coefficient goodness of fit test for the extreme value distribution. Amer. Statistician 43:98–100.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in terms of their power by considering various alternative distributions. Simulation results show that the Kullback–Leibler information test has higher power than some of the studied tests.     

Multivariate Three-Parameter Log-Elliptical Distributions

The three-parameter log-elliptical distribution class is developed for the general situation in which the hypothesis of independence for the elements in a sample is not assumed. The parameter estimators are theoretically showed to be invariant under all distributions in the class by considering only a change in the constant of the scale parameter estimator. An estimation procedure based on the three-parameter lognormal distribution is proposed for the parameter estimation problem in any three-parameter log-elliptical distribution. Two classical lognormal data sets are analyzed without assuming independence in the sample in order to illustrate the proposed estimation procedure.     

Asymptotic Location of Largest Values of a Stationary Random Field

The study of the relationship between extreme values of dependent random fields and their locations has important practical applications, for instance, when dealing with censored data.

In this article we study the asymptotic behavior of the joint locations of the largest order statistics generated by a stationary random field with extremal index as well as the joint limiting distribution of the location of a high level exceedance nearest of the origin and the location of the maximum.     

Predictors of behavioural problems in foster children: the key role of impulsivity

Although several variables have been reported to be associated with behavioural problems in foster children, few studies have sought to establish more precisely the extent to which these variables may explain problematic behaviour. The main aim of this study is to determine the extent to which certain variables may predict behavioural problems shown by foster children. Participants included 104 foster children and their respective foster families. Multiple linear regression analysis revealed that the following variables predict behavioural problems in foster children: impulsivity/attention deficit in the child, level of burden in the foster carers, rigid or authoritarian parental discipline, and criticism/rejection by the foster parents. The model explained 46% of the variance in behaviour problems, with the greatest predictive power (29%) corresponding to the variable ‘impulsivity/attention deficit’. The results show that impulsivity/attention deficit is the most powerful predictor of behavioural problems in foster children. This is consistent with the findings of various studies that have reported an association between a lack of inhibitory control and problematic behaviour.     

Analysis of local influence in geostatistics using Student's t-distribution

This article aims to estimate parameters of spatial variability with Student's t-distribution by the EM algorithm and present the study of local influence by means of two methods known as likelihood displacement and Q-displacement of likelihood, both using Student's t-distribution with fixed degrees of freedom (ν). The results showed that both methods are effective in the identification of influential points.     

Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures

We propose a Bayesian nonparametric instrumental variable approach under additive separability that allows us to correct for endogeneity bias in regression models where the covariate effects enter with unknown functional form. Bias correction relies on a simultaneous equations specification with flexible modeling of the joint error distribution implemented via a Dirichlet process mixture prior. Both the structural and instrumental variable equation are specified in terms of additive predictors comprising penalized splines for nonlinear effects of continuous covariates. Inference is fully Bayesian, employing efficient Markov chain Monte Carlo simulation techniques. The resulting posterior samples do not only provide us with point estimates, but allow us to construct simultaneous credible bands for the nonparametric effects, including data-driven smoothing parameter selection. In addition, improved robustness properties are achieved due to the flexible error distribution specification. Both these features are challenging in the classical framework, making the Bayesian one advantageous. In simulations, we investigate small sample properties and an investigation of the effect of class size on student performance in Israel provides an illustration of the proposed approach which is implemented in an R package bayesIV. Supplementary materials for this article are available online.