Statistical Inference Of Partial Linear Isotonic Regression Models With Several Types Of Data

Partial linear regression model is the combination of parametric regression model and non-parametric regression model. The parametric part can avoid the curse of di-mensionality and improve the explanation of non-parametric part. The non-parametric part can maintain the flexibility of the model. Therefore, in the description of the prac-tical problems, this model has more flexible and explanatory power. In solving practi-cal problems, we often encounter the case that the non-parametric part has obviously monotonic relationship with explanatory variables. On this basis, statisticians raise partially linear monotonic regression model. In real problems, we often encounter the following types of data, such as measurement error data, missing data, Censored data and so on. Therefore, the study of statistical inference method with these types of data under partially linear monotonic regression model has some theoretical significance and Real value.In this thesis, we are mainly concerned with the estimation procedures of the par-tially linear monotonic regression model with several datas including mea-surement error data, missing data, randomly censored data and so on.First, we introduce partially linear monotonic errors-in-variables model.Under this model, we study the estimation of parametric and non-parametric part. We ob-tain the consistent estimation of the Parametric part by using local linear method to estimate the conditional expectation. On this basis, using grouped Brunk B-spline method to obtain the estimation nonparametric part. Under certain regularity condi-tions, we give the asymptotic normality of parametric part and the convergence rate of non-parametric function. We give the finite sample properties of the estimation through simulation experiments. Also, we compare the finite sample properties of the proposed estimators with original estimators through simulation experiments.Second, the estimation of the partially linear monotonic regression model with randomly right censored response and errors in variables is considered.We elevate complete data through making a variable whose mean is as same as response vari-able. The censoring problem is solved. By using local linear method to estimate the conditional expectation, we obtain the (?) consistent estimators of parametric part. By using grouped Brunk B-spline method, we obtain the estimation of nonparametric part.Under certain regularity conditions, we give the asymptotic normality of paramet-ric part and the asymptotic distribution of non-parametric function. We compare the finite sample properties of the proposed estimators with original estimators through simulation experiments under different censoring probabilities.Finally, the estimation of the partially linear monotonic regression model with missing response and errors in variables is considered.We using two-step method in estimating parametric and non-parametric part. Based on the full data, we get the initial estimators of the parametric and nonparametric part by using Local Linear S-moothing method. After that, inverse marginal probability weighted imputation ap-proach is developed to estimate the regression parameter and a least-square approach under monotone constraint is employed to estimate the functional component. It is shown that the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the monotonic estimator of the functional component, at a fixed point,regardless of whether is the boundary point, is cubic root-n consisten-t. We compare the finite sample properties of the proposed estimators with original estimators through simulation experiments under different missing probabilities.