Asymptotic normality of a class of adaptive statistics with applications to synthetic data methods for censored regression. (English) Zbl 0817.62008

Lai, Tze Leung; Ying, Zhiliang; Zheng, Zukang

J. Multivariate Anal. 52, No. 2, 259-279 (1995).

Summary: Motivated by regression analysis of censored survival data, we develop a general asymptotic distribution theory for estimators defined by estimating equations of the form \(\sum^ n_{i=1} \xi (w_ i, \theta, \widehat G_ n) = 0\), in which \(w_ i\) represents observed data

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, \(\theta\) is an unknown parameter to be estimated, and \(\widehat G_ n\) 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

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© Academic Press

MSC:

62E20	Asymptotic distribution theory in statistics
62G20	Asymptotic properties of nonparametric inference
62J99	Linear inference, regression
62G07	Density estimation
60G44	Martingales with continuous parameter

Keywords:

central limit theorem; adaptive estimating equation; von Mises calculus; martingales; asymptotic normality; synthetic least squares estimates; censored regression models; covariance matrices