This paper considers multivariate extension of smooth estimator of the distribution and density function based on Bernstein polynomials studied in Babu et al. [2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. J. Statist. Plann. Inference...

The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be...

A general solution of the Deny convolution equation restricted to a half line is obtained using certain concepts of random walk theory. The equation in question arises in several places in applied probability such as in queueing and storage theories and characterization problems of probability...

Considering a large class of tests, we study higher order power in a possibly non-iid set-up. Optimum properties for the likelihood ratio and score tests are exhibited under the criteria of second-order local maximinity and third-order local average power, respectively. The issue of stringency...

In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector...

It is established that a vector variable (X1, ..., Xk) has a multivariate normal distribution if for each Xi the regression on the rest is linear and the conditional distribution about the regression does not depend on the rest of the variables, provided the regression coefficients satisfy some...

Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical...

Let X be a unit vector random variable taking values on a k-dimensional sphere [Omega] with probability density function f(x). The problem considered is one of estimating f(x) based on n independent observation X1,...,Xn on X. The proposed estimator is of the form fn(x) = (nhk-1)-1C(h)...