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Abstract:
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In this talk, we consider the random design nonparametric regression problem when the response variable is subject to a general mode of missingness or censoring. In such problems, the response variable often must be transformed or truncated in some way for the regression function to remain identifiable. We present a general methodology for imputing responses with the property of double robustness, in that the method works well if either a parameter of the full data distribution (covariate and response distribution) or a parameter of the censoring mechanism is well approximated. We give general results for the method when the imputed responses are entered into commonly used nonparametric regression procedures, including least squares estimators, complexity-regularized least squares estimators, penalized least squares estimators, locally weighted average estimators, and cross-validated estimators.
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