Formulas for covariance matrix between a random vector and its ordered components are derived for different distributions including multivariate normal,t, andF. The present formulas and related results obtained here lead to some known results in the literature as special cases.

We consider anr-dimensional multivariate time series {yt, t[set membership, variant]Z} which is generated by an infinite order vector autoregressive process. We show that a bootstrap procedure which works by generating time series replicates via an estimated finitek-order vector...

In this paper, we consider the problem of approximating the location,x0[set membership, variant]C, of a maximum of a regresion function,[theta](x), under certain weak assumptions on[theta]. HereCis a bounded interval inR. A specific algorithm considered in this paper is as follows. Taking a...

In this note we present a characterization of halfspace depth which relates it with well-known concepts of Locational Analysis. This characterization also leads to a natural extension of the concept of depth to noneuclidean location estimation as well as other settings like regression.

When estimating, under quadratic loss, the location parameter[theta]of a spherically symmetric distribution with known scale parameter, we show that it may be that the common practice of utilizing the residual vector as an estimate of the variance is preferable to using the known value of the...

We address the important practical problem of selecting covariates in mixed linear models when the covariance structure is known from the data collection process and there are a possibly large number of covariates available. In particular, we consider procedures which can be considered...

As restricted canonical correlation with a nonnegativity condition on the coefficients depend only on the covariance matrix, their sample counterparts can be obtained from the sample covariance matrix. For such estimators, asymptotic normality results are established, and the role of resampling...

Multivariate variational inequalities are obtained in terms of thew-functions and the trace of a Fisher-type information matrix. In consequence of these inequalities, the multivariate central limit theorem arises in the sense of the total variation.

This paper considers the multiple linear regression modelYi=xi'[beta]+[var epsilon]i,i=i, ..., n, wherexi's are knownp-1 vectors,[beta]is ap-1 vector of parameters, and[var epsilon]1,[var epsilon]2, ... are stationary, strongly mixing random variables. Let[beta]ndenote anM-estimator...

Let (X1, Y1), (X2, Y2), ..., be two-dimensional random vectors which are independent and distributed as (X, Y). For 0p1, let[xi](p|x) be the conditionalpth quantile ofYgivenX=x; that is,[xi](p|x)=inf{y : P(Y[less-than-or-equals, slant]y|X=x)[greater-or-equal, slanted]p}. We...