For the fixed design regression model, a nonparametric estimate of the probability density function of the residuals is proposed and its basic properties are studied. This estimate should have direct impact on diagnostics of regression models of this type. The estimate proposed here is based on...

In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of...

Using nonparametric kernel estimation method, we propose a consistent test for independence of two random vectors based on the L2 norm of difference between the joint density and the product of their marginals. A Monte Carlo study is carried out to examine the finite sample performance of the...

Some properties of the used better than aged (UBA) and the used better than aged in expectation (UBAE) classes of life distributions are given. These properties include moment inequalities and moment generating functions behavior. In addition, nonparametric estimation and testing of the survival...

Data from multivariate weighted distributions appear in such cases as missing data, damaged data, sociological or economic data. Multivariate kernel density estimation is discussed for these data where its mean square error (pointwise and integrated) is derived and for an important and common...

A class of test statistics is introduced which is based on the Lp-distance between distributions. It is shown to be asymptotically normal both under the null and under the alternatives. The class is easily adaptable to multivariate distributions and to situations when parameters are estimated....

An asymptotically distribution-free test is proposed and studied for testing the null hypothesis H0: Fdisp = G versus H1: Fdisp G, that is G-1([beta])-G-1([alpha])[greater-or-equal, slanted]F-1([beta])-F-1([alpha]) for 0[less-than-or-equals, slant][alpha][beta][less-than-or-equals, slant]1. The...

The degree of approximation of the distance between multinomial and Poisson probabilities has been investigated by Hodges and LeCam (1960) and McDonald (1980). In this note we provide an elementary proof of a bound on the deviation between the multinomial and Poisson probabilities. An extension...