Asymptotically constant risk estimator of the time-average variance constant
针对依赖数据的时间平均方差常数估计难题，提出一种基于收敛平顶核的估计量，其最优带宽渐近地不依赖未知参数，且具有渐近恒定风险和局部渐近极小极大性。
Summary Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top kernels for constructing variance estimators whose optimal bandwidths are free of unknown parameters asymptotically and hence can be computed easily. We prove that the new estimator has an asymptotically constant risk and is locally asymptotically minimax.