Seminars

General Departmental Seminar Series

Minimum Distance Estimation of the Distribution Functions of Stochastically Ordered Random Variables

Ronald Gangnon, Department of Biostatistics and Medical Informatics, UW-Madison

Friday, December 3, 1999, 12:00-1:00 p.m.

E5/584 Clinical Science Center

ABSTRACT

Stochastic ordering can be a natural and minimal restriction in an estimation problem. The standard estimator in such setting is the nonparametric maximum likelihood estimator (NPMLE) subject to the stochastic ordering constraint. The NPMLE is known to be biased, and even when the empirical cdfs nearly satisfy the stochastic orderings, the NPMLE and the empirical cdfs may differ substantially. We propose a minimum distance estimator (MDE) of distribution functions subject to stochastic ordering constraints. We demonstrate the superior small sample performance of the MDE through simulation studies. Two examples of the application of the methodology are provided: analysis of survival times of cancer patients based on degree of lymph node involvement and assessment of grader reliability.

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