The Annals of Statistics

Validity of Blockwise Bootstrap for Empirical Processes with Stationary Observations

U. V. Naik-Nimbalkar and M. B. Rajarshi

Full-text: Open access

Abstract

We show that the empirical process of the block-based bootstrap observations from a stationary sequence converges weakly to an appropriate Gaussian process, conditionally in probability and almost surely, depending upon the block length. This bootstrap was introduced by Kunsch and later by Liu and Singh. Applications in estimation of the sampling distribution of a compactly differentiable functional are indicated.

Article information

Source
Ann. Statist., Volume 22, Number 2 (1994), 980-994.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325507

Digital Object Identifier
doi:10.1214/aos/1176325507

Mathematical Reviews number (MathSciNet)
MR1292552

Zentralblatt MATH identifier
0808.62043

JSTOR
links.jstor.org

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62M99: None of the above, but in this section

Keywords
Bootstrap empirical processes weak convergence stationary and mixing sequences compactly differentiable functionals

Citation

Naik-Nimbalkar, U. V.; Rajarshi, M. B. Validity of Blockwise Bootstrap for Empirical Processes with Stationary Observations. Ann. Statist. 22 (1994), no. 2, 980--994. doi:10.1214/aos/1176325507. https://projecteuclid.org/euclid.aos/1176325507


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