Confidence interval estimation of population means subject to order restrictions using resampling procedures

• Published in: Statistics & probability letters Vol. 31; no. 4; pp. 255 - 265
• Main Author: Peddada, Shyamal Das
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.1997; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Bootstrap; Bootstrap Confidence intervals Coverage probability Jackknife Node Order restriction Pivot Standard error Weighted jackknife; Confidence intervals; Coverage probability; Jackknife; Node; Order restriction; Pivot; Standard error; Weighted jackknife; Confidence intervals; Coverage probability; Order restriction; Jackknife; Node; Bootstrap; Pivot; Standard error; Weighted jackknife
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/S0167-7152(96)00037-5

This article addresses the problem of constructing confidence intervals for ordered population means of k independent normal populations using jackknife and bootstrap methodologies. The goal is to achieve the nominal coverage probability with width of the interval no bigger than that of the standard confidence interval centered at the unrestricted maximum likelihood estimator (UMLE). Confidence intervals considered in this article are based on the point estimator introduced in Hwang and Peddada (1994). The methodology described in this article is applicable to a reasonably broad class of order restrictions. It is seen that the bootstrap procedures such as the percentile method, the BC method and the BC a method fail rather badly, while the confidence intervals based on weighted jackknife performs very well. Simulation studies suggest that the new procedure is robust even if the data are obtained from heavy tailed distributions such as t distribution with very small degrees of freedom.