Mean square consistency and improved rate of convergence of generalized subsampling estimator for non‐stationary time series
研究了非平稳时间序列广义子抽样估计量的均方相合性，证明其满足伯恩斯坦不等式并以改进速率收敛，对周期相关时间序列的傅里叶系数有应用，附模拟验证。
In this article, we show the mean square consistency for a generalized subsampling estimator based on the aggregation of the mean, median, and trimmed mean of some subsampling estimators for general non‐stationary time series. Consistency requires standard assumptions, including the existence of moments and ‐mixing conditions. We apply our results to the Fourier coefficients of the autocovariance function of periodically correlated time series. Furthermore, as in the i.i.d. case, we show that the generalized subsampling estimator satisfies Bernstein inequality and concentrates at an improved rate (under the condition of no or small bias) compared with the original estimator. Finally, we illustrate our results with some simulation data examples.