Combining standardized time series area and Cramér-von Mises variance estimators. (English) Zbl 1126.62078
Summary: We propose three related estimators for the variance parameter arising from a steady-state simulation process. All are based on combinations of standardized time series area and Cramér-von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin-Watson statistic; and the third is related to a jackknifed version of the first. The main derivations yield analytical expressions for the bias and variance of the new estimators. These results show that the new estimators often perform better than the pure area, pure CvM, and benchmark nonoverlapping and overlapping batch means estimators, especially in terms of variance and mean squared error. We also give exact and Monte Carlo examples illustrating our findings.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M09 | Non-Markovian processes: estimation |
| 62G05 | Nonparametric estimation |
| 65C05 | Monte Carlo methods |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
simulation; stationary process; variance estimation; standardized time series; area estimator; Cramér-von Mises estimator; Durbin-Watson estimator; batch means estimatorReferences:
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