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Buckley-James type estimator for censored data with covariates missing by design. (English) Zbl 1246.62114
Summary: The Buckley-James estimator (BJE) is a well-known estimator for linear regression models with censored data. Y. Ritov [Ann. Stat. 18, No. 1, 303–328 (1990; Zbl 0713.62045)] has generalized the BJE to a semiparametric setting and demonstrated that his class of Buckley-James type estimators is asymptotically equivalent to the class of rank-based estimators proposed by A.A. Tsiatis [ibid., 354–372 (1990; Zbl 0701.62051)]. We revisit such relationships in censored data with covariates missing by design. By exploring a similar relationship between our proposed class of Buckley-James type estimating functions to the class of rank-based estimating functions recently generalized by B. Nan, J.D. Kalbfleisch and M. Yu [ibid. 37, No. 5A, 2351–2376 (2009; Zbl 1173.62073)] we establish asymptotic properties of our proposed estimators. We also conduct numerical studies to compare asymptotic efficiencies from various estimators.

MSC:
62G08 Nonparametric regression and quantile regression
62N01 Censored data models
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
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