Universität zu Köln

Bucchia, Beatrice (2014). Testing for epidemic changes in the mean of a multiparameter stochastic process. J. Stat. Plan. Infer., 150. S. 124 - 142. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1873-1171

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Abstract

In this paper, multiparameter stochastic processes {Z(n)(x)}(x is an element of[0, n]d), n is an element of N, are tested for the occurrence of a block (k(0), m(0)] = (k(0,1), m(0,1)] x ... x (k(0,d), m(0,d)] subset of [0, n](d) where the mean of the process changes. This is modeled in the form Z(n)(x) = lambda((0) under bar,x])mu(n) + sigma Y(x)+lambda((0) under bar, x] boolean AND (k(0), m(0)])delta(n) where (0) under bar = (0,..., 0)', lambda(A) denotes the Lebesgue measure of a set A subset of R-d, and mu(n), delta(n) is an element of R as well as 0 < sigma < infinity are unknown parameters. The stochastic process [Y-n(t) = Y ([nt]) : t is an element of[0,1](d)} is assumed to fulfill a weak invariance principle. Under the null hypothesis, an approximation for the tail behavior of the limit variable of a trimmed maximum-type test statistic is given. Then, the (weak) consistency of the test under the alternative is proven. The corresponding estimation problem for the points k(0) and m(0) is also considered and consistent estimators are given for local alternatives delta(n) = delta n(-d/2) with delta not equal 0. (C) 2014 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bucchia, Beatrice UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-434963
DOI:	10.1016/j.jspi.2014.03.001
Journal or Publication Title:	J. Stat. Plan. Infer.
Volume:	150
Page Range:	S. 124 - 142
Date:	2014
Publisher:	ELSEVIER SCIENCE BV
Place of Publication:	AMSTERDAM
ISSN:	1873-1171
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language LONG-RANGE DEPENDENCE; LINEAR RANDOM-FIELDS; CONVERGENCE; STATISTICS Multiple languages Statistics & Probability Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/43496