On construction of prediction intervals for heteroscedastic regression

Abstract

In a real-world regression problem, the variance usually varies with the location, which brings difficulties in prediction of the response. Existing heteroscedastic regression methods suffer from inaccurate estimation and/or high computational complexity, and cannot be used to construct satisfactory prediction intervals for small or large data. This article focuses on the problem of constructing prediction intervals of the response under heteroscedastic regression models. We apply the reconstruction approach to parameterize the mean and variance functions as forms of kernel interpolation, and use the maximum likelihood estimation method to estimate the parameters. Our method allows a small number of parameters in the parameterization forms, and only requires low computational cost. Based on these estimators and some Bayesian modifications, we provide three classes of prediction intervals. Numerical experiments for both small and large datasets indicate that they are very competitive compared with existing heteroscedastic regression methods in terms of coverage rate and computational complexity.

Keywords:

• Interpolation
• Kernel method
• Large data
• Reconstruction parameterization

Acknowledgements

We thank the referees for constructive comments which lead to a significant improvement of this article. This work is supported by the National Natural Science Foundation of China (Grant No. 12171462).

Additional information

Funding

We thank the referees for constructive comments which lead to a significant improvement of this article. This work is supported by the National Natural Science Foundation of China (Grant No. 12171462).