Consistency of the Frequency Domain Bootstrap for differentiable functionals

被引：0

作者：

Bertail, Patrice ^{[1
]}

Dudek, Anna E. ^{[2
]}

机构：

[1] UPL Univ Paris Nanterre, MODAL X, Nanterre, France

[2] AGH Univ Sci & Technol, Dept Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

来源：

ELECTRONIC JOURNAL OF STATISTICS | 2021年 / 15卷 / 01期

关键词：

Bootstrap; empirical process; Frechet differentiability; influence function; second order correctness; spectral density function; spectral measure; REGENERATIVE-BLOCK BOOTSTRAP; TIME-SERIES; RATIO STATISTICS; JACKKNIFE;

D O I：

10.1214/20-EJS1787

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper consistency of the Frequency Domain Bootstrap for differentiable functionals of spectral density function of a linear stationary time series is discussed. The notion of influence function in the time domain on spectral measures is introduced. Moreover, the Frechet and Hadamard differentiability of functionals of spectral measures are defined in the time domain. Sufficient and necessary conditions for consistency of the FDB in the considered problems are provided and the second order correctness is discussed for some functionals. Finally, validity of the FDB for the empirical processes is considered. As an illustration the notions of quantile and range in the time domain are discussed. A simulation study is provided, in which performance of the FDB is analyzed.

引用

页码：1 / 36

页数：36

共 50 条

[1] Differentiable functionals and smoothed bootstrap
Cuevas, A
Romo, J
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1997, 49 (02) : 355 - 370
[2] Differentiable Functionals and Smoothed Bootstrap
Antonio Cuevas
Juan Romo
[J]. Annals of the Institute of Statistical Mathematics, 1997, 49 : 355 - 370
[3] Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals
Beutner, Eric
Zaehle, Henryk
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2016, 10 (01): : 1181 - 1222
[4] ON DIFFERENTIABLE FUNCTIONALS
VANDERVAART, A
[J]. ANNALS OF STATISTICS, 1991, 19 (01): : 178 - 204
[5] Bootstrap consistency for the Mack bootstrap
Steinmetz, Julia
Jentsch, Carsten
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2024, 115 : 83 - 121
[6] ON T-DIFFERENTIABLE FUNCTIONALS
MELNIK, VS
[J]. DOKLADY AKADEMII NAUK, 1992, 324 (05) : 928 - 932
[7] A Multitaper Frequency-Domain Bootstrap Method
Kim, Seong-Eun
Ba, Demba
Brown, Emery N.
[J]. IEEE SIGNAL PROCESSING LETTERS, 2018, 25 (12) : 1805 - 1809
[8] BOOTSTRAP LONG MEMORY PROCESSES IN THE FREQUENCY DOMAIN
Hidalgo, Javier
[J]. ANNALS OF STATISTICS, 2021, 49 (03): : 1407 - 1435
[9] A Bootstrap Attack on Digital Watermarks in the Frequency Domain
Behseta, Sam
Lam, Charles
Webb, Robert L.
[J]. INFORMATION AND COMMUNICATIONS SECURITY, PROCEEDINGS, 2008, 5308 : 361 - +
[10] Frequency domain bootstrap methods for random fields
Ng, Wai Leong
Yau, Chun Yip
Chen, Xinyuan
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2021, 15 (02): : 6586 - 6632

← 1 2 3 4 5 →