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概率统计∣Asymptotic distributions of some scale estimators in the linear regression model with infinite variance long memory errors

编辑:wfy 时间:2019年11月29日 访问次数:129

題目 Asymptotic distributions of some scale estimators in the linear regression model with infinite variance long memory errors 

報告人: Professor Hira L. Koul, Michigan State University

時間: 20191219日(周四)14:00 

地點: 浙江大學玉泉校區歐陽樓316

摘要: 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 d1 , 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.               

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浙江大學數學學院統計系