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Estimation of overflow probabilities...

Harvard University.

Estimation of overflow probabilities for models with heavy tails and complex dependencies.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
書名/作者:	Estimation of overflow probabilities for models with heavy tails and complex dependencies.
作者:	Li, Chenxin.
面頁冊數:	133 p.
附註:	Source: Dissertation Abstracts International, Volume: 70-11, Section: B, page: 6972.
Contained By:	Dissertation Abstracts International70-11B.
標題:	Statistics.
標題:	Operations Research.
ISBN:	9781109496000
摘要、提要註:	Events such as loss packets in queueing systems and bankruptcy probabilities for insurance companies are rare but consequential. The likelihood of such events can often be linked to the maximum of a stochastic process. We refer to such quantities as overflow probabilities---due to their connection to queueing. Current Monte Carlo algorithms for efficient evaluation of overflow probabilities often assume features such as light tails or independence among increments. Our contribution lies in the design and the rigorous statistical analysis of estimators that are applicable to a class of problems with heavy-tailed features or arbitrary dependence structures.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3385460

Estimation of overflow probabilities for models with heavy tails and complex dependencies.
Li, Chenxin.

Estimation of overflow probabilities for models with heavy tails and complex dependencies. - 133 p.

Source: Dissertation Abstracts International, Volume: 70-11, Section: B, page: 6972.

Thesis (Ph.D.)--Harvard University, 2009.

Events such as loss packets in queueing systems and bankruptcy probabilities for insurance companies are rare but consequential. The likelihood of such events can often be linked to the maximum of a stochastic process. We refer to such quantities as overflow probabilities---due to their connection to queueing. Current Monte Carlo algorithms for efficient evaluation of overflow probabilities often assume features such as light tails or independence among increments. Our contribution lies in the design and the rigorous statistical analysis of estimators that are applicable to a class of problems with heavy-tailed features or arbitrary dependence structures.

ISBN: 9781109496000Subjects--Topical Terms:

145349
Statistics.

Estimation of overflow probabilities for models with heavy tails and complex dependencies.
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100 1 $a Li, Chenxin. $3 423509
245 1 0 $a Estimation of overflow probabilities for models with heavy tails and complex dependencies.
300 $a 133 p.
500 $a Source: Dissertation Abstracts International, Volume: 70-11, Section: B, page: 6972.
500 $a Adviser: Jose Blanchet.
502 $a Thesis (Ph.D.)--Harvard University, 2009.
520 $a Events such as loss packets in queueing systems and bankruptcy probabilities for insurance companies are rare but consequential. The likelihood of such events can often be linked to the maximum of a stochastic process. We refer to such quantities as overflow probabilities---due to their connection to queueing. Current Monte Carlo algorithms for efficient evaluation of overflow probabilities often assume features such as light tails or independence among increments. Our contribution lies in the design and the rigorous statistical analysis of estimators that are applicable to a class of problems with heavy-tailed features or arbitrary dependence structures.
520 $a The first part of this dissertation deals with heavy tailed models that exhibit simple correlation. We construct a state-dependent importance sampling estimator for the tail distribution of heavy-tailed compound sums. This is the first provable strongly efficient estimator under basically minimal assumptions within a heavy-tailed environment.
520 $a In the second part, we consider the evaluation of overflow probabilities of Markov random walks. We describe the elements behind the large deviations theory and efficient Monte Carlo estimators in this setting. These elements include the evaluation of certain eigenvalues and eigenfunctions of associated integral operators, which we obtain explicitly for a class of time series models.
520 $a Finally, in third part of dissertation, we study discrete-time Gaussian processes with negative drift and arbitrary dependence structures. In great generality overflow probabilities to a level b for such processes converge to zero exponentially fast in b. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling algorithm, called Target Bridge Sampler (TBS) that estimates the required overflow probability with polynomial complexity in b. This is the first provably efficient estimator for overflow probabilities of Gaussian processes that might exhibit long range dependence. TBS can also be used to generate exact samples for such processes given a large overflow.
590 $a School code: 0084.
650 4 $a Statistics. $3 145349
650 4 $a Operations Research. $3 423094
690 $a 0463
690 $a 0796
710 2 $a Harvard University. $3 423501
773 0 $t Dissertation Abstracts International $g 70-11B.
790 1 0 $a Blanchet, Jose, $e advisor
790 $a 0084
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3385460

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