Efficient simulations for the exponential integrals of Hölder continuous gaussian random fields

Liu, Jingchen; Xu, Gongjun

doi:10.1145/2567892

Cited by 9 publications

(28 citation statements)

References 51 publications

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“…It employs a change of measure defined on the continuous sample space. Similar techniques are used for the extreme analysis of stochastic systems driven by Gaussian processes (Liu and Xu, 2012; Adler, Blanchet and Liu, 2012; Li and Liu, 2015; Liu, Lu and Zhou, 2015; Liu and Xu, 2014a,b).…”

Section: Proof Of Lemmamentioning

confidence: 99%

Chernoff index for Cox test of separate parametric families

Liu

Ying

2018

Ann. Statist.

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The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is also known as the Chernoff index (Chernoff, 1952), a relative efficiency measure when there is no preference between the null and the alternative hypotheses. We further extend the analysis to approximate error probabilities when the two families are not completely separated. Discussions are provided concerning the implications of the present result on model selection.

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Section: Proof Of Lemmamentioning

confidence: 99%

Chernoff index for Cox test of separate parametric families

Liu

Ying

2018

Ann. Statist.

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“…Remark 2. Although the current paper focuses on rare-event simulation for the extremes of Gaussian random fields, the uniform efficiency criterion as well as the proposed method can be easily extended to other Gaussian-related rare-event problems, such as the exponential integrals of Gaussian random fields [e.g., 27,28], where the mean and variance functions are unspecified and we are interested in estimating a family of tail probabilities. Moreover, the proposed method can be extended to the estimation of non-Gaussian tail probabilities.…”

Section: Uniform Efficiencymentioning

confidence: 99%

“…Importance sampling based efficient simulation procedures have been proposed in the literature to estimate the tail probabilities. Numerical methods for rare-event analysis of the suprema were studied in [1,2]; see also [8,20,24,[26][27][28]34] for related studies.…”

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confidence: 99%

Uniformly efficient simulation for extremes of Gaussian random fields

2018

J. Appl. Probab.

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This paper considers the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rareevent simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problem. To overcome this issue, we propose a uniformly efficient estimator for a general family of Hölder continuous Gaussian random fields.We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.

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“…Numerical methods for rare-event analysis of the suprema are studied in [13] and more thoroughly in [12]; see also Azas and Wschebor [14,15]. Simulation study for the exponential integrals of the Gaussian random fields has been studied in Liu and Xu [16,11,17].…”

Section: Introductionmentioning

confidence: 99%

Refinements of Gaussian Tail Inequality

Rather¹,

Rather²

2018

AJPAS

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In this paper, we first prove a theorem which gives considerably better bound for 0 ≤ t ≤ 1/2 than Gaussian tail inequality (or tail bound for normal density) and thus is a refinement of Gaussian tail inequality in this case. Next we present an interesting result which provides a refinement of Gaussian tail inequality for t > √ 3. Besides, we also prove an improvement of Gaussian tail inequality for 0 < t ≤ 1/2. Finally, we present a more general result which includes a variety of interesting results as special cases.

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Efficient simulations for the exponential integrals of Hölder continuous gaussian random fields

Cited by 9 publications

References 51 publications

Chernoff index for Cox test of separate parametric families

Chernoff index for Cox test of separate parametric families

Uniformly efficient simulation for extremes of Gaussian random fields

Refinements of Gaussian Tail Inequality

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