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...

Nonparametric procedures are proposed for testing exponentiality against several new aging classes of life distributions. The main idea is to test if the lifetime of a system, whose failure time has occurred in between visits, belongs to some alternative new aging classes of life distribution....

Let X1,...,Xn be a random sample from a distribution function F. Let Fn(x)=(1/n)[summation operator]i=1nI(Xi[less-than-or-equals, slant]x) denote the corresponding empirical distribution function. The empirical process is defined by In this note, upper bounds are found for E(Dn) and for E(etDn),...

An interesting recent result of [5], Ann. Probability 5, 595-600) is investigated further. Rates of convergence in the conditioned central limit theorem are developed for partial sums and maximum partial sums, with positive mean and zero mean separately, of sequences of independent identically...

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...