A NEW METHOD FOR ESTIMATING LIFE DISTRIBUTIONS FROM INCOMPLETE DATA

• Other Authors: KITCHIN, JOHN FRANCIS.
• Format: Others
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/lib/digcoll/etd/3084762

We construct a new estimator for a continuous life distribution from incomplete data, the Piecewise Exponential Estimator (PEXE). === To date the principal method of nonparametric estimation from incomplete data is the Product-Limit Estimator (PLE) introduced by Kaplan and Meier {J. Amer. Statist. Assoc. (1958) 53}. Our formulation of the estimation problem posed by incomplete data is essentially that of Kaplan and Meier, but we approach its solution from the viewpoint of reliability and life testing. === In this work we establish rigorously the asymptotic (large sample) properties of the PEXE. Our results include the strong consistency of the PEXE under various sets of assumptions plus the weak convergence of the PEXE, suitably normalized, to a Gaussian process. From an intermediate result in our weak convergence proof we derive asymptotic confidence bands and a goodness-of-fit test based on the PEXE. === Though our main objective is the introduction of a new estimator for incomplete data and the study of its asymptotic properties, our second contribution to this area of research is the extension of the asymptotic results of the extensively used PLE. In particular, our results extend the work of Peterson {J. Amer. Statist. Assoc. (1977) 72} and Langberg, Proschan, and Quinzi {Ann. Statist. (1980) 8} in strong consistency and that of Breslow and Crowley {Ann. Statist. (1974) 2} in weak convergence. === Finally, we show that the New PEXE, as an alternative to the traditional PLE, has several advantages for estimating a continuous life distribution from incomplete data, along with some drawbacks. Since the two estimators are so alike asymptotically, we concentrate on differences in the PEXE and the PLE for estimation from small samples. === Source: Dissertation Abstracts International, Volume: 41-08, Section: B, page: 3093. === Thesis (Ph.D.)--The Florida State University, 1980.