Robust estimation and test for Pearson’s correlation coefficient

Abstract

In this paper, using the idea of grouping under moderate data framework, we propose the median-of-means-type nonparametric estimator for Pearson’s correlation coefficient which has been used widely in various disciplines. Under certain conditions on the growing rate of the number of subgroups, the consistency and asymptotic normality of the proposed estimator are investigated. Furthermore, we construct a new method to test Pearson’s correlation coefficient based on the empirical likelihood method for median. Extensively numerical simulations are designed to demonstrate the superiorities of our estimator. It is shown that the new proposed estimator is robust with respect to outliers. Finally, we use the proposed method to study Pearson’s correlation between open price and the rate of price spread for the Shanghai Stock Exchange composite index from 18 May 2015 to 21 June 2019.