It is well known that i.i.d. (independent and identically distributed) normal random variables are transformed into i.i.d. normal random variables by any orthogonal transformation. Less well known are nonlinear transformations with the above-mentioned property. In this work we present nonlinear...

A complete characterization of the spectrum of a locally square integrable periodically correlated (PC) processes is obtained. The result makes use of the author's recent theorem establishing a one to one correspondence between PC processes and a certain class on infinite dimensional stationary...

Consider a long term study, where a series of dependent and possibly censored failure times is observed. Suppose that the failure times have a common marginal distribution function, but they exhibit a mode of time series structure such as [alpha]-mixing. The inference on the marginal...

We consider likelihood based inference in a class of logistic models for case- control studies with a partially observed covariate. The likelihood is a combination of a nonparametric mixture, a parametric likelihood, and an empirical likelihood. We prove the asymptotic normality of the maximum...

The Gauss-Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss-Markov theorem to include nonparametric mixed-effects models. The extended Gauss-Markov estimation (or prediction)...

The Chung-Smirnov law of the iterated logarithm and the Finkelstein functional law of the iterated logarithm for empirical processes are used to establish new results on the central limit theorem, the law of the iterated logarithm, and the strong law of large numbers for L-statistics with...

For a nonnegative strictly stationary random sequence satisfying the "minimal" dependence condition necessary and sufficient conditions for the relative stability are found. As an application the well-known Khinchine stability result for i.i.d. random variables is proved for uniformly strong...

We consider the problem of discriminating, on the basis of random "training" samples, between two independent multivariate normal populations, Np([mu], [Sigma]1) and Np([mu], [Sigma]2), which have a common mean vector [mu] and distinct covariance matrices [Sigma]1 and [Sigma]2. Using the...

The general machinery of Cordeiro and Ferrari (1991, Biometrika78, 573-582) and Chandra and Mukerjee (1991, J. Multivariate Anal.36, 103-112) provides modifications of score test statistics which bring the null distributions close to their large-sample asymptotic distributions. These...

Suppose that the random vector (X1, ..., Xq) follows a Dirichlet distribution on q+ with parameter (p1, ..., pq)[set membership, variant]q+. For f1, ..., fq0, it is well-known that (f1X1+...+fqXq)-(p1+...+pq)=f-p11...f-pqq. In this paper, we generalize this expectation formula...