Second-order correctness of the blockwise bootstrap for stationary observations. (English) Zbl 0906.62040

Götze, F.; Künsch, H. R.

Ann. Stat. 24, No. 5, 1914-1933 (1996).

Summary: We show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second-order correct provided we choose an appropriate variance estimator. We also show how to adapt the \(BC_a\) confidence interval of B. Efron [J. Am. Stat. Assoc. 82, 171-200 (1987; Zbl 0622.62039)] to the dependent case. For the proofs we extend the results of F. Götze and C. Hipp [Z. Wahrscheinlichkeitstheor. Verw. Geb. 64, 211-239 (1983; Zbl 0514.60027)] on the validity of the formal Edgeworth expansion for a sum to the studentized mean.

MSC:

62G09	Nonparametric statistical resampling methods
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G15	Nonparametric tolerance and confidence regions
62E20	Asymptotic distribution theory in statistics

Keywords:

time series; strong mixing; blockwise bootstrap approximation; dependent data; confidence interval; Edgeworth expansion

Citations:

Zbl 0622.62039; Zbl 0514.60027