Many of the popular nonparametric test statistics for censored
survival data used in two-sample, $k$-sample trend and continuous covariate
situations are special cases of a general statistic, differing only in the
choice of the covariate-based label and the weight function. A weight function
determines the asymptotic efficiency of its corresponding statistic in this
general class. Since the true alternatives are often unknown, we may not be
able to foresee which weight function is the best for a particular data set. We
show in this paper that certain large families of these statistics form
stochastic processes, doubly indexed by both the weight function and the time
scale, which converge weakly to Gaussian processes also indexed by both the
weight function and the time scale. These asymptotic properties allow
development of versatile test procedures which are simultaneously sensitive to
a reasonably large collection of alternatives. Due to the complexity of the
Gaussian processes, a Monte Carlo approach is proposed to obtain the
distributional characteristics of these statistics under the null
hypothesis.
Publié le : 1999-10-14
Classification:
Survival analysis,
censored data,
contiguous alternatives,
counting process,
function-indexed stochastic process,
martingale,
Monte Carlo method,
nonparametric,
weak convergence,
62G10,
60F05,
60G44,
62E25
@article{1017939149,
author = {Lin, Chin-Yu and Kosorok, Michael R.},
title = {A general class of function-indexed nonparametric tests for
survival analysis},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1722-1744},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939149}
}
Lin, Chin-Yu; Kosorok, Michael R. A general class of function-indexed nonparametric tests for
survival analysis. Ann. Statist., Tome 27 (1999) no. 4, pp. 1722-1744. http://gdmltest.u-ga.fr/item/1017939149/