Nonparametric testing against restricted alternatives under progessive censoring

Abstract

Nonparametric testing procedures under progressive censoring schemes are often adopted in clinical trials and life testing experimentations. In a variety of situations, a null hypothesis (of the homogeneity of distributions) may be tested against a restricted viz., orthant or ordered alternative. Though such tests in a general setup have been considered in a complete sample or a single point censored (or truncated) experimental scheme, there has not been much progress with these tests in a progressively censored setup. Genuinely distribution free tests based on simple linear rank statistics and the classical union intersection principle are considered. The theory of such time sequential tests rests heavily on some basic invariance principles, and these are studied as well. The case of proportional hazard models is also treated briefly. The main emphasis is laid on the development of the relevant asymptotic theory, and in this context, some (sub) martingale characterizations of progressively censored rank statistics have been incorporated.

Keywords:

• Bessel-bar process
• invariance principles
• Kuhn-Tucker-Lagrange formula
• linear rank statistics
• linear regression model
• ordered and orthant (restricted) alternatives
• progressive censoring schemes
• proportional hazard model
• time-sequential tests
• union-intersection principle