Asymptotically Constant Risk Estimator of the Time-Average Variance Constant

• Activity Number: 510 - Recent Development in Semiparametric and Nonparametric Methods
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Chun-Yip Yau*
• Companies: Chinese University of Hong Kong
• Keywords: Asymptotic variance; bandwidth selection; kernel estimator; locally asymptotically minimax; long-run variance; tuning-free

Abstract

Estimation of the asymptotic variance of a time-average, which is known as the time-average variance constant (TAVC), or long run variance, is important for many statistical procedures involving dependent data. However, the estimation of TAVC is difficult as its performance relies heavily on the choice of a bandwidth parameter. Specifically, the optimal choices of bandwidth of all existing estimators depend on the TAVC itself and another unknown parameters which is very difficult to estimate. Thus, the optimal estimation of TAVC is not achievable. In this paper, by introducing a novel concept of converging kernel, we develop a new class of TAVC estimators in which the optimal bandwidth is free of unknown parameters and hence can be computed easily. Moreover, we prove that the new estimator has a constant risk asymptotically, in contrast to the exploding risk in the existing estimators.