Minimum distance conditional variance function checking in heteroscedastic regression models

Assessing the adequacy of variance function in heteroscedastic regression models.

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is ...

Approximately unbiased estimation of conditional variance in heteroscedastic kernel ridge regression

In this paper we extend a form of kernel ridge regression for data characterised by a heteroscedastic noise process (introduced in Foxall et al. [1]) in order to provide approximately unbiased estimates of the conditional variance of the target distribution. This is achieved by the use of the leave-one-out cross-validation estimate of the conditional mean when fitting the model of the condition...

Robust Estimation of Conditional Mean by the Linear Combination of Quantile Regressions

In this paper, we propose a new robust estimator for regression problems in the form of the linear combination of quantile regressions. The proposed robust regression estimator is helpful for the conditional mean estimation especially when the error distribution is asymmetric or/and heteroscedastic, where conventional robust regressions yield considerable bias to the conditional mean. First we ...

Asymptotic 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...

Variance Function Estimation in Heteroscedastic Regression Models