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In this paper, the authors study the partially linear single-index model when the covariate X is measured with additive error and the response variable Y is sometimes missing. Based on the least-squared technique, an imputation method is proposed to estimate the regression coefficients, single-index coefficients, and the nonparametric function, respectively. Thereafter, asymptotical normalities of the corresponding estimators are proved. A simulation experiment and an application to a diabetes study are used to illustrate our proposed method.
Qi et al. (Mon,) studied this question.