The Annals of Statistics

Asymptotic Results for Inference Procedures Based on the $r$ Smallest Observations

Richard A. Johnson

Full-text: Open access

Abstract

We consider procedures for statistical inference based on the smallest $r$ observations from a random sample. This method of sampling is of importance in life testing. Under weak regularity conditions which include the existence of a q.m. derivative for the square root of the ratio of densities, we obtain an approximation to the likelihood and establish the asymptotic normality of the approximation. This enables us to reach several important conclusions concerning the asymptotic properties of point estimators and of tests of hypotheses which follow directly from recent developments in large sample theory. We also give a result for expected values which has importance in the theory of rank tests for censored data.

Article information

Source
Ann. Statist., Volume 2, Number 6 (1974), 1138-1151.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342870

Digital Object Identifier
doi:10.1214/aos/1176342870

Mathematical Reviews number (MathSciNet)
MR418313

Zentralblatt MATH identifier
0295.62041

JSTOR
links.jstor.org

Subjects
Primary: 62F99: None of the above, but in this section

Keywords
Asymptotic inference censored data life testing

Citation

Johnson, Richard A. Asymptotic Results for Inference Procedures Based on the $r$ Smallest Observations. Ann. Statist. 2 (1974), no. 6, 1138--1151. doi:10.1214/aos/1176342870. https://projecteuclid.org/euclid.aos/1176342870


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