Ratio tests for variance change in nonparametric regression

Abstract

In this paper, we propose a ratio test to detect the variance change in the nonparametric regression models under both fixed and random design cases. The asymptotic validity of detection procedure is derived and its finite sample performance is evaluated via a simulation study. Compared with the existing cumulative sums (CUSUM) test in the literature, our ratio test does not need to estimate any scale parameter. In particular, the ratio test performs significantly better than those in the literature when variance shifts from a large value to a small value. Finally, we illustrate our method in practice by analysing a set of China stock data and a set of light detection and ranging data.

Keywords:

• ratio test
• nonparametric regression
• variance change

AMS Subject Classifications:

• 62F03
• 62G08

Acknowledgements

We are grateful to the editors and referees for useful suggestions and helpful comments for improving the paper. We also thank the Professor Rupert who provided the LIDAR data used in Section 4.2. This work was supported by the National Natural Science Foundation of China (No.60972150) and the Science and Technology Innovation Foundation of Qinghai Normal University (2012).