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Chengjie Xiong

Bio: Chengjie Xiong is an academic researcher from Washington University in St. Louis. The author has contributed to research in topics: Probability distribution & Consistent estimator. The author has an hindex of 1, co-authored 1 publications receiving 4 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a binary search procedure was proposed to detect the changepoints in the sequence of the ratios of probabilities and obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the probability ratio sequence has a changepoint.
Abstract: This article studies the problem of testing and locating changepoints in likelihood ratios of two multinomial probability vectors. We propose a binary search procedure to detect the changepoints in the sequence of the ratios of probabilities and obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the probability ratio sequence has a changepoint. We also give a strongly consistent estimator for the changepoint location. An information theoretic approach is used to test the equality of two discrete probability distributions against the alternative that their ratios have a changepoint. Approximate critical values of the test statistics are provided by simulation for several choices of model parameters. Finally, we examine a real life data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and locate the changepoints in the probability ratios.

5 citations


Cited by
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Journal ArticleDOI
TL;DR: A best contrast approach and an alternative approach based on order-restricted information criteria for the model selection of a particular exposure-response relationship are introduced.
Abstract: One possibility for the statistical evaluation of trends in epidemiological exposure studies is the use of a trend test for data organized in a 2 × k contingency table. Commonly, the exposure data are naturally grouped or continuous exposure data are appropriately categorized. The trend test should be sensitive to any shape of the exposure-response relationship. Commonly, a global trend test only determines whether there is a trend or not. Once a trend is seen it is important to identify the likely shape of the exposure-response relationship. This paper introduces a best contrast approach and an alternative approach based on order-restricted information criteria for the model selection of a particular exposure-response relationship. For the simple change point alternative H1 : π1 = ...= πq <πq+1 = ... = πk an appropriate approach for the identification of a global trend as well as for the most likely shape of that exposure-response relationship is characterized by simulation and demonstrated for real data examples. Power and simultaneous confidence intervals can be estimated as well. If the conditions are fulfilled to transform the exposure-response data into a 2 × k table, a simple approach for identification of a global trend and its elementary shape is available for epidemiologists.

16 citations

Book ChapterDOI
22 May 2005
TL;DR: This paper focuses on a statistical method aiming at detecting changepoint as quickly as possible using Bayes factor along with the binary segmentation procedure modified for fast detection.
Abstract: Detection of network problems is an important step in automating network management. Early detection of performance degradation can alleviate the last moment hassel of network managers. This paper focuses on a statistical method aiming at detecting changepoint as quickly as possible using Bayes factor along with the binary segmentation procedure modified for fast detection. Computer simulation verifies the effectiveness and correctness of the proposed approach.

6 citations

Journal ArticleDOI
TL;DR: In this article, stochastic orderings based on the failure rate function and likelihood ratio are discussed for non-negative integer valued random variables, and it is expected that the results presented could inspire further work on this little-researched area.
Abstract: SYNOPTIC ABSTRACTThere has been little known with respect to stochastic orderings of discrete random variables. In this note, stochastic orderings based on the failure rate function and likelihood ratio are discussed for non-negative integer valued random variables. It is expected that the results presented could inspire further work on this little–researched area.

4 citations

Journal ArticleDOI
TL;DR: In this paper , tests based on U-statistics are proposed to test for equality of marginal density functions against the alternative of likelihood-ratio ordered when ( X , Y ) are dependent.
Abstract: Abstract Characterisation of marginal distribution and density functions is of interest where data on a pair of random variables ( X , Y ) are observed. Stochastic orderings between ( X , Y ) have been studied in statistics and economics. Likelihood-ratio ordering is useful in understanding the behaviour of the random variables. In this article, tests based on U-statistics are proposed to test for equality of marginal density functions against the alternative of likelihood-ratio ordered when ( X , Y ) are dependent. The tests can be used when the data are either completely observed or subjected to independent univariate right censoring. The asymptotic variances of these tests are complicated and hence, are estimated using jackknife variance estimators. Validity of the jackknife variance estimators in statistical inference based on the proposed tests is demonstrated using simulation studies. The test for uncensored setting has desired size and good power for small sample. The performance of the tests for censored case depends on the sample size, proportion of censoring and the measure of dependence between X and Y . The tests are illustrated on three real data sets chosen in order to bring out various aspects of the tests.

1 citations