Semiparametric Regression With Missing Values

Sri Haryatmi Kartiko
Math Dept, UGM, Yogyakarta, Indonesia

Abstract
Semiparametric regression deals with several covariates which has parametric relation with the response and one other covariate which has nonparametric relation with the response. This natural compromise between the linear model and the fully nonparametric model, is to allow only some of the predictors to be modelled linearly and the rest being modelled nonparametrically such as the following,
Yi = Xi'Beta+g(Ti)+Ei
However in the real world, often not all responses are available for various reason such as unwillingness of some respondents to supply the desired information, lost of information by uncontrollable factors and so forths. We consider the case where some Y values in a sample of size n may be missing but X and T are completely observed. That is we obtain the incompleteobservation (Yi,alfai,Xi, Ti), i = 1, . . . , n for the stated model, where all the Xi and Ti are observed and delta = 0 if Yi is missing and otherwise deltai = 0, here Y is missing at random.
This paper deals with inference of the mean of Y under regression imputation of missing responses based on the semiparametric regression model and uses semiparametric regression imputation scheme and semiparametric techniques to develop an adjusted empirical likelihood and partially smoothed bootstrap empirical likelihood.

Keywords: semiparametric regression, missing at random, regression imputation, empiricallikelihood, bootstrap.

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