Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Parametric Tests and Estimation of Mean Change in Discrete Distributions

  • Kim, Jae-Hee (Department of Statistics, Duksung Women's University) ;
  • Cheon, Soo-Young (KU Industry-Academy Cooperation Group Team of Economics and Statistics, Korea University)
  • Published : 2009.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

We consider the problem of testing for change and estimating the unknown change-point in a sequence of time-ordered observations from the binomial and Poisson distributions. Including the likelihood ratio test, Gombay and Horvath (1990) tests are studied and the proposed change-point estimator is derived from their test statistic. A power study of tests and a comparison study of change-point estimators are done via simulation.

Keywords

References

  1. Chen, J. and Gupta, A. K. (2000). Parametric Statistical Change Point Analysis, Birkhauser, Berlin
  2. Fitzgibbon, L. J., Dowe, D. L. and Allison, L. (2002). Change-point estimation using new minimum message length approximations, Lecture Notes In Computer Science, 2417, 244-254
  3. Gombay, E. and Horvath, L. (1990). Asymptotic distributions of maximum likelihood tests for change in the mean, Biometrika, 77, 411-414 https://doi.org/10.1093/biomet/77.2.411
  4. Hawkins, D. M. (2001). Fitting multiple change-point models to data, Computational Statistics and Data Analysis, 37, 323-341 https://doi.org/10.1016/S0167-9473(00)00068-2
  5. Hinkley, D. V. and Hinkley, E. A. (1970). Inference about the change-point in a sequence of binomial random variables, Biometrika, 57, 477-488 https://doi.org/10.1093/biomet/57.3.477
  6. Perry, M. B. and Pignatiello, J. R. (2008). A change point model for the location parameter of expo-nential family densities, lEE Transactions, 40, 947-956 https://doi.org/10.1080/07408170701775102
  7. Pettit, A. N. (1980). A Simple cumulative sum type statistics for the change-point problem with zero-one observations, Biometrika, 67, 79-84 https://doi.org/10.1093/biomet/67.1.79
  8. Simpkin, J. M. and Downham, D. Y. (2006). Testing for a change-point in registry data with an example on hypospadias, Statistics in Medicine, 7, 387-393 https://doi.org/10.1002/sim.4780070304
  9. Worsley, K. J. (1983). The power of likelihood ratio and cumulative sum tests for a change in a binomial probability, Biometrika, 70, 455-464 https://doi.org/10.1093/biomet/70.2.455