Chi-square goodness-of-fit test for randomly censored data. (English) Zbl 0633.62041

Habib, M. G.; Thomas, D. R.

Ann. Stat. 14, 759-765 (1986).

The problem of testing goodness of fit of a parametric family \(\{F(\cdot,\theta), \theta\in\Theta\}\) of survival distributions from arbitrary right-censored data is considered. Weak convergence of the process \(\sqrt{N}[\hat F_ N(\cdot)-F(\cdot,{\hat \theta}_ N)]\) is obtained where \(\hat F_ N\) is a Kaplan-Meier estimator and \({\hat \theta}_ N\) is a maximum likelihood estimator of the parameter \(\theta\). Asymptotic distributions of the modified Pearson statistic and the generalized Pearson statistic are obtained both for nonrandom partitions and partitions with random boundaries.

Reviewer: R.Mnatsakanov

MSC:

62G10	Nonparametric hypothesis testing
62F03	Parametric hypothesis testing
62E20	Asymptotic distribution theory in statistics
60F05	Central limit and other weak theorems

Keywords:

chi-square test; product-limit process; testing goodness of fit; survival distributions; right-censored data; Weak convergence; Kaplan-Meier estimator; maximum likelihood estimator; modified Pearson statistic; generalized Pearson statistic; nonrandom partitions; partitions with random boundaries