Improving the estimators of the parameters of a probit regression model: A ridge regression approach

This paper considered the estimation of the regression parameters of a general probit regression model. Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters (β)$(\beta )$ when the weighted design matrix is ill-conditioned and it is suspected that the parameter β$\beta$ may belong to a linear subspace defined by Hβ=h$H\beta =h$. Asymptotic properties of the estimators are studied with respect to quadratic biases, MSE matrices and quadratic risks. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Some relative efficiency tables and risk graphs are provided to illustrate the numerical comparison of the estimators. We conclude that when q≥3$q\ge 3$, one would uses PRRRE; otherwise one uses PTRRE with some optimum size α$\alpha$. We also discuss the performance of the proposed estimators compare to the alternative ridge regression method due to Liu (1993).     

Sexual deviancy: diagnostic and neurobiological considerations

Individuals who engage in sexual offenses may be afflicted with a paraphilic disorder or sexual deviation syndrome. Paraphilias are psychiatric disorders characterized by deviant and culturally non-sanctioned sexual fantasies, thoughts, and/or behaviors. A proportion of these individuals may also suffer from symptoms of mental illness that can go unrecognized. Although the etiology and pathophysiology of paraphilic disorders continue to be under investigation, data from empirical, biomedical, and psychopharmacological studies suggest abnormalities at a biological level. This article will discuss and review clinical and neurobiological characteristics of the paraphilias. To this end, we will begin with a general exploration and overview of basic principles that are germane to the subject matter and will conclude with an examination of the most recent relevant research findings.     

On the structural estimation of certain correlation coefficients

In this paper, the estimation of a real-valued function of the parameter by minimizing the expected value of the quadratic loss function relative to the structural distribution of the parameter is proposed; this is called structural estimation. The general formulae developed have been used to obtain the structural estimate of the bivariate correlation coefficient and of the intraclass correlation coefficient.     

Simultaneous estimation of several CDF’s: homogeneity constraint

Let {x_ij(1 ? j ? n_i)|i = 1, 2, …, k} be k independent samples of size n_j from respective distributions of functions F_j(x)(1 ? j ? k). A classical statistical problem is to test whether these k samples came from a common distribution function, F(x) whose form may or may not be known. In this paper, we consider the complementary problem of estimating the distribution functions suspected to be homogeneous in order to improve the basic estimator known as “empirical distribution function” (edf), in an asymptotic setup. Accordingly, we consider four additional estimators, namely, the restricted estimator (RE), the preliminary test estimator (PTE), the shrinkage estimator (SE), and the positive rule shrinkage estimator (PRSE) and study their characteristic properties based on the mean squared error (MSE) and relative risk efficiency (RRE) with tables and graphs. We observed that for k ? 4, the positive rule SE performs uniformly better than both shrinkage and the unrestricted estimator, while PTEs works reasonably well for k < 4.