Regression estimation for bivariate normal distributions

Abstract

SummaryIn estimating the mean /~v of one variable in a bivariate normal distribution, the experimenter can use the other variable, ~, as an auxiliary variable to increase precision. In particular, if /~x is known, he can use the regression estimator. When /~= is unknown, a preliminary test can be performed and the estimator will be made to depend on the result of the preliminary test. The bias and mean square error of the preliminary test estimator are obtained and the relative efficiency is are discussed.

Multi-auxiliary regression estimation based on conditional specification

“…The bias was also studied by Han [7] who expressed it in terms of the cumulative distribution function of the standard normal distribution. Therefore we have As a partial check, when c--0, we always reject the null hypothesis and use ~ and B~=O.…”

“…Without loss of generality, we let ~v22= I and a~--1. The values of e~ and e~ for p--1 are given in Han [7]. The bias was also studied by Han [7] who expressed it in terms of the cumulative distribution function of the standard normal distribution.…”

“…Preliminary test estimator was first studied by Bancroft [1] and later by Bennett [3], [4], Han [7], [8], Han and Bancroft [10], Kale and Bancroft [12], Kitagawa [13], Mosteller [15] and others. It is known that the yield is highly correlated with the moisture and nitrogen content of the soil.…”

“…Han [7] studied the estimator Y* when p--1. : is the 100(1--a) percentage point of the Chi-squared distribution with p degrees of freedom and a is the level of significance of the preliminary test.…”

Regression estimation for multivariate normal distributions

“…The present thesis is divided into three main parts. The first part is an effort to extend the studies of Han (1973a) for bivariate normal distributions to (pifl) variate normal distributions (p+1 > 2). The second part attempts to extend the method of double sampling with partial information on auxiliary variables first studied by Han (1973b) for one auxiliary variable to the case where the auxiliary variable is a pxl vector.…”