Some lower bounds for the variance of a function g of a random vector X are extended to a wider class of distributions. Using these bounds, some useful inequalities for the Fisher information are obtained for convolutions and linear combinations of random variables. Finally, using these...

Two methods are suggested for removing the problem of negativity of high-order kernel density estimators. It is shown that, provided the underlying density has at least moderately light tails, each method has the same asymptotic integrated squared error (ISE) as the original kernel estimator....

This paper treats strong convergence of adaptive multivariate recursive M-estimators of location when the scatter matrices are unknown. The observations are elliptically distributed and form a strictly stationary strong mixing sequence. The main algorithm handles a recursive estimator of...

In this paper some ideas on experimental designs are used in discriminant analysis. By considering the populations as groups, one may classify a new observation by minimizing a suitable norm of the within groups sum of squares and cross products matrix after assigning it to each group. The...

Restricted maximum likelihood (REML) estimation is a method employed to estimate variance-covariance parameters from data that follow a Gaussian linear model. In applications, it has either been conjectured or assumed that REML estimators are asymptotically Gaussian with zero mean and variance...

Assuming a general linear model with known covariance matrix, several linear and nonlinear predictors are presented and their properties are discussed. In the context of simultaneous multiple prediction, a total sum of squared errors is suggested as a loss function for comparing predictors....

Let {Xt; t [set membership, variant] 0} be a strictly stationary process with mean zero and autovariance function (a.c.v.f.) [gamma]v, v [set membership, variant] 0. Let [gamma]v = n - 1 [summation operator]n - vt = 1 be the serial covariance of order v computed from a sample X1, ..., Xn drawn...

It is shown by an example that in general, the rate of bootstrap approximation to the studentized sample mean of lattice data is not better than the rate in the case of the normalized sample mean. A modified bootstrap method is proposed and shown to be second-order correct. Unlike the...

A Monte Carlo power study of 10 multivariate normality goodness-of-fit tests is presented. First, multivariate goodness-of-fit methods and non-normal alternatives are classified according to their characteristics. Then, a measurement tool is defined, validated, and used to assess the performance...

Several inequalities of Kahane-Khintchine's type in certain Orlicz spaces are proved. For this, the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, the third...