Change-Point Problems in a Sequence of Binomial Variables

  • Jeong, Kwang-Mo (Department of Statistics, Research Institute of Information and Communication, Pusan National University)
  • Published : 1996.08.01

Abstract

For the Change-point problem in a sequence of binomial variables we consider the maximum likelihood estimator (MLE) of unknown change-point. Its asymptotic distribution is quite limited in the case of binomial variables with different numver of trials at each time point. Hinkley and Hinkley (1970) gives an asymptotic distribution of the MLE for a sequence of Bernoulli random variables. To find the asymptotic distribution a numerical method such as bootstrap can be used. Another concern of our interest in the inference on the change-point and we derive confidence sets based on the liklihood ratio test(LRT). We find approximate confidence sets from the bootstrap distribution and compare the two results through an example.

Keywords

References

  1. Nonparametric Statistics v.5 Change-Point Problem and Bootstrap Antoch, J.;Huskova, M.
  2. Nonparametric Statistics v.3 A Nonparametric Bootstrapped Estimate of the Change-Point Boukai, B.
  3. Biometrika v.65 The Problem of the Nile: Conditional Solution to a Change-Point Problem Cobb, G. W.
  4. Journal of the American Statistical Association v.82 Comment on "Better Bootstrap Confidence Intervals" by Efron, B. Cox, D. R.
  5. The Annals of statistics v.19 The Asymptotic behaviour of some nonparametric change-Point Estimators Dumbgen, L.
  6. Biometrika v.72 Bootstrap Confidence Intervals for a Class of Parametric Problems Efron, B.
  7. Biometrika v.57 Inference About the Change-Point in a Sequence of random variables Hinkley, D. V.
  8. Biometrika v.57 Inference about the Change-Point in a Sequence of Binomial Variables Hinkley, D. V.;Hinkley, E. A.
  9. Biometrika v.74 Conditional Bootstrap Methods in the Mean-Shift Model Hinkley, D. V.;Schechtman, E.
  10. Applied statistics v.28 A Nonparametric Approach to the Change-Point Problem Pettitt, A. N.
  11. Biometrika v.67 A Simple Cumulative Sum Type statistic for the Change-Point Problem with Zero-One Observations Pettitt, A. N.
  12. Biometrika v.73 Bayesian Analysis of a Poisson Process with a Change-Point Raferty, A. E.;Akman, V. E.
  13. Journal of the Royal Statistical Society B v.20 Philological Probability Problems Ross, A. S. C.
  14. International Statistical Review v.56 Confidence Sets in Change-Point Problems Siegmund, D.
  15. Biometrika v.62 A Bayesian Approach to Inference about a Change-Point in a Sequence of random variables Smith, A. F. M.
  16. Biometrika v.70 The Power of Likelihood ratio and Cumulative Sum Tests for a Change in a Binomial Probability Worsley, K. J.
  17. Biometrika v.73 Confidence regions and Tests for a Change-Point in a Sequence of Exponential Family Random Variables Worsley, K. J.