It is a common situation in biomedical research that one or more variables are known to be associated with the outcome of interest. Researchers often discretize some variables and fit a regression model using these discretized variables. Although convenient for illustration purposes, such an...

We prove that if the Tukey depths of two atomic measures are identical, then the measures are also identical.

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n-1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of...

The covariance between the functions of two random variables is obtained in terms of the cumulative distribution function. This result generalizes previous formulae given by W. Hoeffding (1940, Schriften Math. Inst. Univ. Berlin5, 181-233) and K. V. Mardia (1967, Biometrika54, 235-249). An...

In estimating the variogram of a spatial stochastic process, we use a spatial design matrix. This matrix is the key to Matheron's variogram estimator. We show how the structure of the matrix for any dimension is based on the one-dimensional spatial design matrix, and we compute explicit...

Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method utilized for this procedure is to embed the spherical distribution quantile transformation of each...

This paper gives a unified treatment of the limit laws of different measures of multivariate skewness and kurtosis which are related to components of Neyman's smooth test of fit for multivariate normality. The results are also applied to other multivariate statistics which are built up in a...

Statistical depth functions are being used increasingly in nonparametric multivariate data analysis. In a broad treatment of depth-based methods, Liu, Parelius, and Singh ("Multivariate analysis by date depth: Descriptive statistics, graphics and inference (with discussion)," 1999) include...

The randomized play-the-winner (RPW) rule is very useful in clinical trials for patient allocation with two treatments. L. J. Wei (1979, Ann. Statist.7, 291-296) introduces the generalized Friedman's urn (GFU) model to clinical trials of K treatments (as an extension of the RPW). In this paper,...

Srivastava gave an asymptotically efficient and consistent sequential procedure to obtain a fixed-width confidence region for the mean vector of any p-dimensional random vector with finite second moments. For normally distributed random vectors, Srivastava and Bhargava showed that the specified...