Asymptotic Properties of the Nonparametric Part in Partial Linear Heteroscedastic Regression Models
نویسنده
چکیده
This paper considers estimation of the unknown function g() in the partial linear regression model Y i = X T i + g(T i) + " i with heteroscedastic errors. We rst construct a class of estimates g n of g and prove that, under appropriate conditions, g n is weak, mean square error consistent. Rates of convergence and asymptotic normality for the estimator g n are also established.
منابع مشابه
Differenced-Based Double Shrinking in Partial Linear Models
Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...
متن کاملEfficient semiparametric estimator for heteroscedastic partially linear models
We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asy...
متن کاملA Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression
Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares es...
متن کاملAsymptotic Normality of Parametric Part in Partial Linear Heteroscedastic Regression Models
Consider the partial linear heteroscedastic model Y i = X T i + g(T i) + i e i ; 1 i n with random variables (X i ; T i) and response variables Y i and unknown regression function g(). We assume that the errors are heteroscedastic, i.e., 2 i 6 = const: e i are i.i.d. random error with mean zero and variance 1. In this partial linear heteroscedastic model, we consider the situations that the var...
متن کاملAsymptotic Inference in Some Heteroscedastic Regression Models with Long Memory Design and Errors
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in th...
متن کامل