The K-d Estimation In The Semiparametric Regression Model

It is well known that semiparametric regression models overcome some defectsof parameters and non-parametric models. After the semiparametric regression modelsare put forward, they are applied in many fields. This paper systematically studied thek-d estimation in a semiparametric regression model.In chapter2, we give the k-d estimation in the semiparametric regression model.First, the distribution of the ridge parameter estimator is discussed. Second, thedefinition of k-d estimation is given in the semiparametric regression model, andthe distributions of k and d estimators are researched. Third, under the conditions ofthe mean squares errors, we proved that k-d estimators are better than Liu’sestimators, which are given by Duran et.al.(2011). At last, it is illustrated our resultsby a practical application.In chapter3，we discuss the generalized k-d estimators in the semiparametricregression model, which are extended of some results in chapter2.And it is comparedwith the classical least square estimation under the conditions of the mean squareserrors. In addition, we give the generalized Liu’s estimators in the semiparametricregression model, which is a special case of the generalized k-d estimator in asemiparametric regression model. At last, we give two applications to illustrated thesuperiority of the estimator under the conditions of the mean squares errors.