New Recursive Estimators of The Time-average Variance Constant
Chan, K. W. & Yau, C. Y. (2016). New Recursive Estimators of The Time-average Variance Constant. Statistics and Computing, 26, 609-627.
Abstract
Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC withO(1) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with O(1) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the O(1) memory complexity and is better than Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is 1.12 times that of the optimal off-line TAVC estimator.
- Main Paper
- Supplementary Material
- R-code
- Poster Presentation (The 59th ISI Young Statisticians Meeting, 23-24 August 2013)
- Publisher Website
Figure: Graphical illustration of recursive batches selection rules.
- (TRI): Existing method; see Wu, W. B. (2009, AoAP).
- (TSR) & (PSR): Proposed methods.