A New Nonparametric Estimation Method of the Variance in Heteroscedastic Model

A New Nonparametric Estimation Method of the Variance in a Heteroscedastic Model

In most economic phenomena, the assumption of homoscedasticity in the classic linear regression model is not necessarily true, which leads to heteroscedasticity. The heteroscedastic estimate is an important aspect for the problem of heteroscedasticity. For this hot issue, this paper proposes a nonparametric estimation method with simple calculation for the estimation of heteroscedasticity throu...

Optimal Difference-based Variance Estimation in Heteroscedastic Nonparametric Regression

Estimating the residual variance is an important question in nonparametric regression. Among the existing estimators, the optimal difference-based variance estimation proposed in Hall, Kay, and Titterington (1990) is widely used in practice. Their method is restricted to the situation when the errors are independent and identically distributed. In this paper, we propose the optimal difference-b...

Adaptive Variance Function Estimation in Heteroscedastic Nonparametric Regression

We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. Th...

A 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...

Variance Function Estimation in Heteroscedastic Regression Models