Least Squares Life Statistics Without Lifetimes

• Activity Number: 175
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Laurence L. George*+ and Mark A. Felthauser
• Companies: Problem Solving Tools and TRIAD
• Keywords: estimation ; least squares ; survival function ; reliability ; failure rate ; actuarial

Abstract

Often, data are not iid and may be available only in grouped form (e.g., shipment and return counts of manufactured products). When measurements on individual units are lacking and the data are not iid, a different approach is required in order to make useful survival function estimates. This paper discusses the properties of the nonparametric least squares survival function estimator (nplse) from grouped birth and death counts. Assume Y=X*b+e, where Y=deaths, X=births, and e is a discrete Weiner process, where X(j) is the number of births in successive, contiguous intervals and Y(j) are deaths from X(1),...,X(j). The Gauss-Markov theorem (G-M) applies to unconstrained OLS, but survival functions are constrained. The empirical distribution of estimators is always computable from data subsets. The G-M theorem extends to Weiner error process for unconstrained OLS [Giordano and Tsu]. The Kuhn-Tucker theorem justifies unrestricted, all-subsets regression to find the nplse [Waterman]. Results appear to be normal and BLUE. Computing the nplse from successively larger data subsets gives changepoint information.