DOI QR코드

DOI QR Code

Test and Estimation for Normal Mean Change

  • Kim, Jae-Hee (Department of Statistics, Duksung Women's University) ;
  • Ryu, Jong-Eun (Division of Epidemiology and Health Index Assistant Researcher, Center for Genome Science, National Institute Health, Korea Center for Disease Control & Prevention(KCDC))
  • Published : 2006.12.31

Abstract

We consider the problem of testing the existence of change in mean and estimating the change-point when the data are from the normal distribution. A change-point estimator using the likelihood ratio test statistic, Gombay and Horvath (1990) test statistic, and nonparametric change-point estimator using Carlstein (1988) empirical distribution are studied when there exists one change-point in the mean. A power study is done to compare the change test statistics. And a comparison study of change-point estimators for estimation capability is done via simulations with S-plus software.

Keywords

References

  1. Bhattacharya, G.K. and Johnson, R.A. (1968). Nonparametric Tests for Shift at an Unknown Time Point. Annals of Mathematical Statistics, Vol. 39, 1731-1743 https://doi.org/10.1214/aoms/1177698156
  2. Buckley, M.J. (1991). Detecting a Smooth Signal: Optimality of Cusum based Procedures. Biometrika, Vol. 78, 2 253-262 https://doi.org/10.1093/biomet/78.2.253
  3. Carlstein, E. (1988). Nonparametric Change-point Estimation. Annals of Statistics, Vol. 16, 188-197 https://doi.org/10.1214/aos/1176350699
  4. Chen, Jie and Gupta, A.K. (2000). Parametric Statistical Change Point Analysis. Birkhauser, Berlin
  5. Chernoff, H. and Zacks, S. (1964). Estimating the Current Mean of a Normal Distribution Which is Subject to Changes in Time. Annals of Mathematical Statistics, Vol. 35, 999-1028 https://doi.org/10.1214/aoms/1177700517
  6. Gardner, L.A. (1969). On Detecting Change in the Mean of Normal Variates. Annals of Mathematical Statistics, Vol. 40, 116-126 https://doi.org/10.1214/aoms/1177697808
  7. Gombay, E. and Horvath, L. (1990). Asymptotic Distributions of Maximum Likelihood Tests for Change in the Mean. Biometrika, Vol. 77, 411-414 https://doi.org/10.1093/biomet/77.2.411
  8. Gombay, E. and Horvath, L. (1996). Approximations for the Time of Change and the Power Function in Change-point Models. Joumal of Statistical Planning and Inference, Vol. 52, 43-66 https://doi.org/10.1016/0378-3758(95)00025-9
  9. Hawkins, D.M. (1977). Testing a Sequence of Observations for a Shift in Location. Journal of American Statistical Association, Vol. 72, 180-186 https://doi.org/10.2307/2286934
  10. Hinkley, D.V. (1970). Inference about the Change-point in a Sequence of Random Variables. Biometrika, Vol. 57. 1-16 https://doi.org/10.1093/biomet/57.1.1
  11. James, B., James, K.L. and Siegmund, D. (1987). Tests for a Change-point. Biometrika, Vol. 74, 71-83 https://doi.org/10.1093/biomet/74.1.71
  12. Kander, A. and Zacks, S. (1966). Testing Procedures for Possible Changes in Parameters of Statistical Distributions Occurring at Unknown Time Points. Annals of Mathematical Statistics, Vol. 37, 1196-1210 https://doi.org/10.1214/aoms/1177699265
  13. Page, E.S. (1955). A Test for a Change in a Parameter Occurring at an Unknown Point. Biometrika, Vol. 42, 523-527 https://doi.org/10.1093/biomet/42.3-4.523
  14. Sen. A.K. and Srivastava, M.S. (1975). On Tests for Detecting Change in Mean. Annals of Statistics, Vol. 3, 98-108 https://doi.org/10.1214/aos/1176343001
  15. Worsley, K.J., (1979). On the Likelihood Ratio Test for a Shift in Location of Normal Populations. Joumal of American Statistical Association, Vol. 74, 365-377 https://doi.org/10.2307/2286336
  16. Yao, Y.C. and Davis, R.A. (1986). The Asymptotic Behavior of the Likelihood Ratio Statistic for Testing Shift in Mean in a Sequence of Independent Normal Variates. Sankhya, 339-353