Testing Epidemic Changes of Infinite Dimensional Parameters

Račkauskas, Alfredas; Suquet, Charles

doi:10.1007/s11203-005-0728-5

Cited by 25 publications

(11 citation statements)

References 12 publications

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“…The problem of detecting a change in the mean of a sequence of Banach‐space‐valued random elements has recently been approached from a theoretical angle by Rackauskas and Suquet (2006). Motivated by detecting an epidemic change (the mean changes and then returns to its original value), Rackauskas and Suquet (2006) proposed an interesting statistic based on increasingly fine dyadic partitions of the index interval and derived its limit, which is non‐standard.…”

Section: Introductionmentioning

confidence: 99%

Detecting Changes in the Mean of Functional Observations

Berkes

Gabrys

Horváth

et al. 2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

147

188

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Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as "X" "i" ("t")="μ"("t")+Σ 1≤"l">&infin ; "η" "i", "l" + "v" "l" ("t "), where "μ" is the common mean, "v" "l" are the eigenfunctions of the covariance operator and the "η" "i", "l" are the scores. Inferential procedures assume that the mean function "μ"("t") is the same for all values of "i". If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of principal component analysis are confounded by the change(s). It is therefore important to develop a methodology to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from England. Copyright (c) 2009 Royal Statistical Society.

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Section: Introductionmentioning

confidence: 99%

Detecting Changes in the Mean of Functional Observations

Berkes

Gabrys

Horváth

et al. 2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

147

188

View full text Add to dashboard Cite

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“…We are going to consider the hypotheses on linearity or homoscedasticity of an econometric models which were considered, e.g., by Chow [2,3], Galdfeld and Quandt [6], Joshi [10,11], Maddala [13], Račkauskas [16], Račkauskas and Suquet [17].…”

Section: Testing Linearity or Homoscedasticity Of Regression Functionmentioning

confidence: 99%

“…So, it is a problem of testing homogeneity of the expected value. The outlined hypotheses are tested by several known procedures like those considered, e.g., in [2,3,6,8,16,17,[19][20][21]. Below an another test useful for testing such a type hypotheses is proposed and analyzed its stochastic properties as well as its applications.…”

Section: Introduction and Notationmentioning

confidence: 99%

Testing Homogeneity of Variance or Expected Value in Sequence of Independent Normal Distributions

Wywiał

2009

Acta Appl Math

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The hypothesis of variance and expected value homogeneity of a sequence of independent normal variable is considered. A statistic to testing this hypothesis is proposed. Its moments are derived. Unbiasedness of the test as well as the limit theorem about the test statistic distribution is proved. Approximation of the test statistic probability distribution is evaluated. On the basis of computer simulation some critical values of the test are determined and the power of the test is analyzed. Several applications of the test are proposed, too.

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“…, X n,n be a triangular array of independent random elements in E. There exist s * n and t * n such that for 1 ≤ i ≤ ns * n or nt * n < i ≤ n, the X i,n 's have distribution P n , while for ns * n < i ≤ nt * n , they have distribution Q n . We refer to e.g., Avery and Henderson [1], Commenges et al [3], Račkauskas and Suquet [12,13], Yao [17] for a comprehensive review. Our aim to this model is to estimate the pair (s * n , h * n ), where h * n = t * n − s * n measures the length of the changed segment.…”

Section: Introductionmentioning

confidence: 99%