D G Kabe

Theory of sample surveys

Simple Random Sampling Sampling with Varying Probabilities of Selection Stratified Sampling Systematic Sampling Ratio Method of Estimation Regression Method of Estimation Cluster Sampling Sub-Sampling Two-Stage and Three-Stage Sampling Double Sampling Non-Sampling Errors.

On a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectures that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency, This conjecture is proved to be correct.

NON-SAMPLING ERRORS

It is a general assumption in the sampling theory that the true value of each unit in the population can be obtained and tabulated without any errors. In practice, this assumption may be violated due to several reasons and practical constraints. This results in errors in the observations as well as in the tabulation. Such errors which are due to the factors other than sampling are called non-sampling errors.

On Selberg’s beta integrals

Askey and Richards (1989) evaluate Selbergs first and second beta integrals using Aomotos (1987) formidable methodology of setting and solving a first order difference equation. Using this methodology they evaluate certain other beta and gamma type integrals. However, Selbergs first and second beta and gamma type integrals very elegantly fit within the framework of hypercomplex multivariate normal distribution theory developed by Kabe (1984), and hence can be evaluated using the known multivariate normal distribution theory integrals.

On a zonal polynomial integral

A certain multiple integral occurring in the studies of nBeherens-Fisher multivariate problem has been evaluated by Mathai net al. (1995) in terms of invariant polynomials. However, this npaper explicitly evaluates the context integral in terms of zonal npolynomials, thus establishing a relationship between zonal npolynomial integrals and invariant polynomial integrals.

On the impact of equicorrelated responses on multicollinearity

Given the Gauss-Markov rnodel unknown and ω having the intraclass correlation.structure, Ali and Ali (1992) study the impact of the structure of ω on the expected value of . The present paper examines the impact of the assumed equicorrelation structure of ω on the expected value of ,and generalizes some expected squared length values inequalities derived by Ali and Ali (1992).

Some results for a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectured that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency. This conjecture was proved correct by Kabe and Gupta for a wrong choice of constant covariance matrix. The present paper demonstrates that this loss of efficiency persists even with an estimated covariance matrix, thereby resulting in inefficient estimation, prediction, and confidence intervals.

On a multiple correlation ratio

A squared multiple correlation ratio of a random vector y on another random vector x is defined by [eta]2(y,x)=V(E(yx))/V(y). The advantages of the present multiple correlation ratio over the one defined by Sampson (1984) are pointed out.