Nonlinear principal components are defined for normal random vectors. Their properties are investigated and interpreted in terms of the classical linear principal component analysis. A characterization theorem is proven. All these results are employed to give a unitary interpretation to several...

Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the...

We consider a problem of nonparametric density estimation under shape restrictions. We deal with the case where the density belongs to a class of Lipschitz functions. Devroye [L. Devroye, A Course in Density Estimation, in: Progress in Probability and Statistics, vol. 14, Birkhuser Boston Inc.,...

There are many ways to measure the dispersion of a random variable. One such method uses the concept of peakedness. If the random variable X is symmetric about a point [mu], then Birnbaum [Z.W. Birnbaum, On random variables with comparable peakedness, The Annals of Mathematical Statistics 19...

We study in this paper the extremal behavior of stochastic integrals of Legendre polynomial transforms with respect to Brownian motion. As the main results, we obtain the exact tail behavior of the supremum of these integrals taken over intervals [0,h] with h0 fixed, and the limiting...

In this paper, we consider a technique called the generic Principal Component Analysis (PCA) which is based on an extension and rigorous justification of the standard PCA. The generic PCA is treated as the best weighted linear estimator of a given rank under the condition that the associated...

We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cramer-von Mises test statistic. Finite sample properties are...

In this paper, a family of kurtosis orderings for multivariate distributions is proposed and studied. Each ordering characterizes in an affine invariant sense the movement of probability mass from the "shoulders" of a distribution to either the center or the tails or both. All even moments of...

Copula as an effective way of modeling dependence has become more or less a standard tool in risk management, and a wide range of applications of copula models appear in the literature of economics, econometrics, insurance, finance, etc. How to estimate and test a copula plays an important role...

The problem of quadratic prediction for population quadratic quantities in finite populations has been considered in the literature. In this paper, we mainly aim at extending the ordinary quadratic prediction problems to a general case, and derive the representations of the two essentially...