Asymptotic Inference for a Change-Point Poisson Process

Akman, Varol; Raftery, Adrian E.

doi:10.1214/aos/1176350178

Cited by 36 publications

(25 citation statements)

References 16 publications

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“…Readers who are interested in interval estimates are encouraged to follow up on the references provided. [7][8][9]12,13 Results Figure 1 shows the number of fatal crashes per month in New Zealand, between January 1990 and December 1997, that involved at least one male driver under the age of 25. The change-point was estimated to be around December 1992.…”

Section: Methodsmentioning

confidence: 99%

Fatal crashes involving young male drivers: a continuous time Poisson change‐point analysis

Tay

2001

Australian and New Zealand Journal of Public Health

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Background : In an effort to reduce road trauma, the New Zealand government implemented a series of intervention programs over the last decade, with young male drivers as the main target audience. Previous research, however, found little or no evidence that these programs had any impact on this group of drivers despite an apparent decrease in their crash involvement. Objective : To determine the approximate time when the decrease in the number of fatal crashes involving young male drivers occurred. Method : A Poisson change‐point estimator was used to locate the most likely point where a decrease in the average number of monthly crashes had occurred. Results : The most likely time of change was found to coincide with the time when the Transport Act 1992 was debated and passed in Parliament. The publicity given to the issue and the Government's signal of impending actions were sufficient to induce a significant change in the behaviours of young male drivers. Implications : This result can partially reconcile the difference between the apparent reduction in the number of fatal crashes involving young male drivers and the inability of previous studies to find a significant impact of the various intervention programs since the change occurred prior to the actual implementation of the programs. Nevertheless, it was argued that the implementation of the programs subsequently was necessary in sustaining the reduction.

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Section: Methodsmentioning

confidence: 99%

Fatal crashes involving young male drivers: a continuous time Poisson change‐point analysis

Tay

2001

Australian and New Zealand Journal of Public Health

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“…In this case, (117, 131) and (x 117 , x 131 ) are the confidence intervals at the 95 % significance level for the index event and time event of the changepoint, respectively. This interval is somewhat shorter that the ones given by Akman and Raftery (1986), Raftery and Akman (1986) and Green (1995). The estimated expected value between consecutive accidents are λ 1 = 114.83 and λ 2 = 391.54 in both periods, respectively.…”

Section: A Real Data Examplementioning

confidence: 71%

“…Maguire et al (1952), Akman and Raftery (1986), Worsley (1986) and Siegmund (1988) gave frequentist analysis by proposing several statistics to test for one changepoint at a given location. Lately, most of the works dealing with changepoints in Poisson processes are from a Bayesian perspective.…”

Section: Introductionmentioning

confidence: 99%

The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

Galeano

2007

Computational Statistics & Data Analysis

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This paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example. Keywords AbstractThis paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example.

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“…There are many studies on the single change point in random variable sequences such as binomial, normal, exponential, and gamma (Hinkley, 1970;Hinkley and Hinkley, 1970;Akman and Raftery, 1986;Worsley, 1986;Haccou et al, 1988;West and Ogden, 1997;Jandhyala and Fotopoulos, 1999;Boudjellaba et al, 2001;Fotopoulos and Jandhyala, 2001;Jandhyala and Fotopoulos, 2001;Yigiter, 2006). Besides, the multiple change point problem is considered in many studies, for instance, Hendersen and Matthews (1993) studied multiple change points in Poisson random variables sequences and applied to the annual number hemolytic uremia syndrome cases.…”

Section: Estimation Of Change Points In Sequences Of Poisson Random Vmentioning

confidence: 99%

Estimation of change point and compound Poisson process parameters for the earthquake data in Turkey

2008

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SUMMARYThe existence of change point in the Turkish earthquake data is investigated. For this purpose, the 218 earthquake data of magnitude 5 and higher, between the north (39.00-42.008) and the east (26.00-45.008) coordinates in Turkey from 12 July 1900 to 28 February 2007 are used. The characteristic function of the magnitude is derived. Poisson distribution is used to describe the recurrence times. In addition, using the compound Poisson process, the expected value and variance are estimated and computed for the loss of life and damaged buildings after the change point.

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Asymptotic Inference for a Change-Point Poisson Process

Cited by 36 publications

References 16 publications

Fatal crashes involving young male drivers: a continuous time Poisson change‐point analysis

Fatal crashes involving young male drivers: a continuous time Poisson change‐point analysis

The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

Estimation of change point and compound Poisson process parameters for the earthquake data in Turkey

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