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Sequential test and change point pro...

Kim, Dong-Yun.

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Sequential test and change point problems with staggered entry.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sequential test and change point problems with staggered entry./
作者:	Kim, Dong-Yun.
面頁冊數:	93 p.
附註:	Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2737.
Contained By:	Dissertation Abstracts International64-06B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3096125

Sequential test and change point problems with staggered entry.
Kim, Dong-Yun.

Sequential test and change point problems with staggered entry. - 93 p.

Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2737.

Thesis (Ph.D.)--University of Michigan, 2003.

In part I we derive a non-linear renewal theorem for random walks that are perturbed by an approximately stationary sequence. As corollaries, we obtain the limiting joint distribution of the excess over the boundary and last perturbation, along with an approximation to expected first passage times. We illustrate the results by an analysis of a sequential probability ratio test when data are subject to both censoring and staggered entry.Subjects--Topical Terms:

517247
Statistics.

Sequential test and change point problems with staggered entry.
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245 1 0 $a Sequential test and change point problems with staggered entry.
300 $a 93 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2737.
500 $a Chair: Michael Woodroofe.
502 $a Thesis (Ph.D.)--University of Michigan, 2003.
520 $a In part I we derive a non-linear renewal theorem for random walks that are perturbed by an approximately stationary sequence. As corollaries, we obtain the limiting joint distribution of the excess over the boundary and last perturbation, along with an approximation to expected first passage times. We illustrate the results by an analysis of a sequential probability ratio test when data are subject to both censoring and staggered entry.
520 $a We show that the random walk perturbed by an approximately stationary sequence and a slowly changing sequence can be used to model the log-likelihood ratio test statistic in a two-sample scenario.
520 $a In part II we study the problem of change point in the hazard rate of the exponential distribution when the data are subject to type I censoring and staggered entry. We consider a test for change point in a closed interval and we show that the normalized log-likelihood ratio test statistic can be approximated by the absolute value of a process which converges weakly to a non-stationary Gaussian process. We also show that the limiting process, after a suitable time transformation, becomes an Ornstein-Uhlenbeck process. We use the approximation formula for the tail probability of the process to compute the critical values of the test and study the power by computer simulation.
520 $a Finally, we construct a confidence interval for a change point based on the log-likelihood function. To do so, we first show that the local log-likelihood ratio process converges weakly to a Gaussian process and derive the distribution of the supremum of that process. Using the inverse map of the log-likelihood ratio function evaluated at fine grid points, we obtain a confidence interval for the change point. We study the coverage probability of the interval by simulation and comment on the use of smoothing to improve the excessive coverage problem and reduce the average length of the confidence interval.
590 $a School code: 0127.
650 4 $a Statistics. $3 517247
650 4 $a Biology, Biostatistics. $3 1018416
690 $a 0463
690 $a 0308
710 2 0 $a University of Michigan. $3 777416
773 0 $t Dissertation Abstracts International $g 64-06B.
790 1 0 $a Woodroofe, Michael, $e advisor
790 $a 0127
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3096125