Abstract #302047

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JSM 2003 Abstract #302047
Activity Number: 395
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: SSC
Abstract - #302047
Title: Estimators of Regression Parameters with Missing Data: Reweighting the Score
Author(s): Cyntha Anne Struthers*+ and Don L. McLeish
Companies: University of Waterloo and University of Waterloo
Address: Dept. of Stat. and Actuarial Science, Waterloo, ON, N2L 3G1, Canada
Keywords: missing data ; weighted score ; regression
Abstract:

It is common in applications of regression for one or more covariates to be unobserved for some of the experimental subjects, either by design (for example they are expensive or difficult to obtain) or by some random censoring mechanism. For example in a two-stage experiment, a preliminary analysis may determine for which observations we should obtain complete data. Suppose Y is a response variable with a density function f(y|x,v;b ) where x and v are vectors and b is a vector of unknown parameters. We discuss the estimation of the parameter b when data on the covariate v are available for all observations but the covariate x is missing for some. We assume that x is "missing at random," i.e., that the probability that x is missing depends only on the fully observed quantities (y,v). Variations on this problem have been considered by Chatterjee et al., 2003; Lawless et al., 1999; Reilly and Pepe, 1995; Carrol and Wand, 1991; and Pepe and Fleming, 1991. We suggest and compare several easily implemented estimators for this problem when the data are discrete or continuous. In certain cases, substantial bias is evident, and we suggest alternatives with smaller bias.

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