Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression

Motivated by regression analysis of censored survival data, we develop herein a general asymptotic distribution theory for estimators defined by estimating equations of the form [summation operator]ni=1[xi] (wi, [theta], Gn) = 0, in which wi represents observed data, [theta] is an unknown parameter to be estimated, and Gn represents an estimate of some unknown underlying distribution. This general theory is used to establish asymptotic normality of synthetic least squares estimates in censored regression models and to evaluate the covariance matrices of the limiting normal distributions.