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Lower functions of empirical processes and brownian sheets. / Lifshits, M. A.; Shi, Z.

In: Theory of Probability and its Applications, Vol. 48, No. 2, 03.08.2004, p. 273-287.

Research output: Contribution to journal › Article › peer-review

Harvard

Lifshits, MA & Shi, Z 2004, 'Lower functions of empirical processes and brownian sheets', Theory of Probability and its Applications, vol. 48, no. 2, pp. 273-287. https://doi.org/10.1137/S0040585X97980397

APA

Lifshits, M. A., & Shi, Z. (2004). Lower functions of empirical processes and brownian sheets. Theory of Probability and its Applications, 48(2), 273-287. https://doi.org/10.1137/S0040585X97980397

Vancouver

Lifshits MA, Shi Z. Lower functions of empirical processes and brownian sheets. Theory of Probability and its Applications. 2004 Aug 3;48(2):273-287. https://doi.org/10.1137/S0040585X97980397

Author

Lifshits, M. A. ; Shi, Z. / Lower functions of empirical processes and brownian sheets. In: Theory of Probability and its Applications. 2004 ; Vol. 48, No. 2. pp. 273-287.

BibTeX

@article{6ffc68f569714213b46061e73a80b446,
title = "Lower functions of empirical processes and brownian sheets",
abstract = "We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: Find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986].",
keywords = "Brownian sheet, Empirical process, Infinite-dimensional brownian motion, Lower function, Rate of escape",
author = "Lifshits, {M. A.} and Z. Shi",
year = "2004",
month = aug,
day = "3",
doi = "10.1137/S0040585X97980397",
language = "English",
volume = "48",
pages = "273--287",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "Society for Industrial and Applied Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - Lower functions of empirical processes and brownian sheets

AU - Lifshits, M. A.

AU - Shi, Z.

PY - 2004/8/3

Y1 - 2004/8/3

N2 - We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: Find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986].

AB - We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: Find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986].

KW - Brownian sheet

KW - Empirical process

KW - Infinite-dimensional brownian motion

KW - Lower function

KW - Rate of escape

UR - http://www.scopus.com/inward/record.url?scp=2142661599&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97980397

DO - 10.1137/S0040585X97980397

M3 - Article

AN - SCOPUS:2142661599

VL - 48

SP - 273

EP - 287

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 2

ER -

ID: 37012059