Chengjie Xiong

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.

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.

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.

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.