Nonparametric Hypothesis Testing and Confidence Intervals with Doubly Censored Data

Mai Zhou and Kun Chen

Abstract:

The non-parametric maximum likelihood estimator (NPMLE) of the distribution function with doubly censored data can be computed using self-consistent algorithm (Turnbull, 1978). We extend the self-consistent algorithm to include a constraint on the NPMLE. We then show how this can be used to construct confidence intervals and test hypotheses based on the NPMLE via empirical likelihood ratio. Finally we present some numerical comparison of the performance of the above method with another method that make use of the influence functions.

Keywords: Self consistency, Empirical likelihood, Influence function, Asymptotic chi-square distribution

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