Showing papers on "Coverage probability published in 1971"

Asymptotic Behavior of a Class of Confidence Regions Based on Ranks in Regression

Abstract: Asymptotic behavior of a class of confidence regions, based on rank statistics, for the regression parameter vector is considered. These regions are shown to be asymptotically bounded and ellipsoidic in probability. Asymptotic normality of their center of gravities is also proved. It is noted that the asymptotic efficiencies of these regions when defined in terms of ratio of Lebesgue measures corresponds to that of corresponding test statistics that are used to define these regions. Similar conclusion holds for their center of gravities, where now asymptotic efficiency is defined as inverse ratio of their generalized limiting variances. Also a class of consistent estimators is given for some functionals of the underlying distributions. Finally simultaneous confidence intervals, based on the above center of gravity, for linear parametric functions are shown to have asymptotic coverage probability $1 - \alpha$. Basic to this work are two papers, one by the author [4] and one by Jureckova [3].

On Fixed-Width Confidence Bounds for Regression Parameters

Abstract: In this paper Chow and Robbins' (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for the linear regression parameters under weaker conditions than Srivastava (1967), Albert (1966), and Gleser (1965). An extension to multivariate case has also been carried out.

Interval estimation of the ordered means of two normal populations based on hybrid estimators

Abstract: SUMMARY The interval estimation of ordered means of two normal populations based on a statistic which is sometimes the pooled sample mean and sometimes the maximum, or minimum, of the sample means, depending on whether the difference between the two sample means is small or large, when the two sample means have a common known variance is considered. The coverage probability of this procedure is derived and its behaviour is investigated. Comparisons with other procedures are made.