Showing papers on "Coverage probability published in 1981"
TL;DR: In this paper, the authors discuss two sequential procedures for constructing confidence intervals for the mean with a relative width requirement, and compare their small-sample performances on a variety of stochastic models for which analytic results are available.
Abstract: In this paper we discuss two sequential procedures for constructing confidence intervals for the mean with a relative width requirement. Carefully stating the procedure proposed by Nadas and the procedure considered by Thomas, Iglehart, Robinson, Lavenberg and Sauer, and Law, we give some efficiency and consistency results concerning the latter, and compare their small-sample performances on a variety of stochastic models for which analytic results are available.
40 citations
TL;DR: In this paper, Ghosh and DasGupta derived the rate of convergence of the coverage probability for estimating the mean of a U-statistic through Sproule's(1969, 1974) procedure.
Abstract: Csenki(1980a) utilized the rate of convergence results of Landers and Rogge(1976b) for suitably normalized random means to obtain the rate of convergence of the coverage probability for Chow-Robbins'(1965) fixed-width confidence interval procedure. In this paper, we utilize the rate of convergence results of Ghosh and DasGupta(1980) for suitably normalized random U-statistics to derive the rate of convergence of the coverage probability for estimating the mean of a U-statistic through Sproule's(1969, 1974) procedure. We show that Csenki's(1980a) convergence rate can be achieved with a substantial economy on moment condition. We also propose a two-stage procedure for this pro-1970 AMS Classification: 60F05, 62L10, 62G10
15 citations
TL;DR: In this article, a semi-circular region Φn={(a,b)':b>0} of radiusd was proposed for simultaneous estimation of the mean and variance of a normal distribution.
Abstract: The problem of simultaneous estimation of the mean and variance of a normal distribution has been studied. We propose a semi-circular region Φn={(a,b)':b>0} of radiusd, which has approximately a preassigned coverage probability. Asymptotic efficiency and asymptotic consistency (asd→0) of our proposed sequential procedures have been proved.
3 citations
TL;DR: In this article, a Monte Carlo analysis of the coverage probability of a real-valued function of the unknown parameters θ and φ is presented, and the authors suggest a sequential procedure which gives a fixed-width confidence interval for g(θ, φ) so that the coverage probabilities are approximately α (preas-signed).
Abstract: Summary
Let X1…, Xm and Y1…, Yn be two independent sequences of i.i.d. random variables with distribution functions Fx(.|θ) and Fy(. | φ) respectively. Let g(θ, φ) be a real-valued function of the unknown parameters θ and φ. The purpose of this paper is to suggest a sequential procedure which gives a fixed-width confidence interval for g(θ, φ) so that the coverage probability is approximately α (preas-signed). Certain asymptotic optimality properties of the sequential procedure are established. A Monte Carlo study is presented.