Venue：Room 306 Ouyang Chunmei Building, Yuquan Campus
Abstract：
Typically M estimators of regression parameters in the linear regression model are robust against heavy tails of the error distributions, but not scale invariant. To make them scale invariant one often uses the two robust scale parameter estimators, median of the absolute residuals s1 and the median of the absolute differences of pairwise residuals s2 in the definitions of these M estimators. Since M estimators are robust against heavy tail error distributions, it is natural to know if s1 and s2 are consistent under heavy tail error distribution assumptions. This talk will present their limiting distributions when the regression errors form a linear long memory moving average stationary process with α-stable (1 < α < 2) innovations, where the moving average coefficients aj ～ j d−1 , 0 < d < 1 − 1/α. It turns out that s2 has an α∗-stable limit distribution with α∗ = α(1 − d) < α while the consistency rate of s1 is generally worse than that of s2. In the case of symmetrically distributed errors, there is no difference in their consistency rate. The proof is based on the 2nd order asymptotic expansion of the empirical process of the stated infinite variance stationary sequence.
Contact Person: SU Zhonggen(suzhonggen@zju.edu.cn)