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Semi-parametric and Structured Nonparametric Modeling with Censored Responses Open Access

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Because of non-negativity or detection limit, data with fixed censored responses iscommon in econometrics and biometrics studies. When the response variable is fixedcensored, to explore the relationship between the response variable and predictor covariates,several estimation methods have been proposed in the literature. However,most of the current existing estimation methods assume a linear model between theresponse variable and predictor variables, which is restrictive in practice. Though fewnonparametric regression models were discussed to relieve the linearity assumption,these nonparametric models unfortunately suffer from "curse of dimensionality".To capture the possible nonlinear relationship and avoid "curse of dimensionality"at the same time, in this dissertation, we propose several new semi-parametric andstructured nonparametric models to analyze data with fixed censoring. These modelsinclude single-index models with fixed censored responses, additive models withfixed censored responses and single-index models with varying coefficient index withfixed censored responses. Under some regularity conditions, the estimators of theparametric and nonparametric components in these models are shown to have desiredstatistical properties, such as consistency and asymptotic normality. Simulation studiesshow that our proposed estimators perform well in finite sample experiments. HIVdata sets are analyzed by using the proposed models for illustration.

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