Asymptotic behavior of two-sample rank tests in the presence of random censoring. (English) Zbl 0544.62048

Leurgans, Sue

Ann. Stat. 12, 572-589 (1984).

Summary: Two samples, \(\{X_{ji}\), 1\(\leq i\leq n(j)\} (j=1,2)\) are assumed to be composed of i.i.d. random variables with survival functions \((1-F_ j)(1-H_ j)\), where H is the c.d.f. of the ”censoring times” and F is the c.d.f. of the ”true lifetimes”. A unified derivation of Pitman efficiencies of a class of rank statistics for censored samples is presented.
The conditions under which the result holds do not require contiguous alternatives, since convergence to normality is shown to hold uniformly in equicontinuous \((F_ 1,F_ 2,H_ 1,H_ 2)\) with bounded hazard rates. The uniformity is obtained by studying a convenient joint representation of several counting processes. The results are applied to the translated exponential distributions, a noncontiguous family of alternatives.

MSC:

62G20	Asymptotic properties of nonparametric inference
62E20	Asymptotic distribution theory in statistics

Keywords:

two-sample rank tests; survival functions; censoring times; true lifetimes; unified derivation of Pitman efficiencies; censored samples; convergence to normality; counting processes; translated exponential distributions; noncontiguous family of alternatives