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2014 | 34 | 1-2 | 51-62
Tytuł artykułu

A Bayesian significance test of change for correlated observations

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EN
Abstrakty
EN
This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.
Twórcy
  • Departemnet of Mathematics and Computer Science, University of Adrar, National Road No. 06, Adrar, Algeria
  • Departement of Probability and Statistics, USTHB, P.O. Box 32 EL Alia 16111 Bab Ezzouar, Algiers, Algeria
Bibliografia
  • [1] M.M. Barbieri and C. Conigliani, Bayesian analysis of autoregressive time series with change points, J. Italian Stat. Soc. 7 (1998) 243-255. doi: 10.1007/BF03178933
  • [2] R.L. Brown, J. Durbin and J.M. Evans, Techniques for testing the constancy of regression relationships over time (with discussion), J.R. Statist. Soc. A 138 (1975) 149-63.
  • [3] H. Chernoff and S. Zacks, Estimating the current mean distribution which is subjected to change in time, Ann. Math. Statist. 35 (1964) 999-1018. doi: 10.1214/aoms/1177700517
  • [4] D. Ghorbanzadeh and R. Lounes, Bayesian analysis for detecting a change in exponential family, Appl. Math. Comp. 124 (2001) 1-15. doi: 10.1016/S0096-3003(00)00029-1
  • [5] H.-J. Kim, Change-point detection for correlated observations, Statistica Sinica 6 (1996) 275-287.
  • [6] A. Kander and S. Zacks, Test procedure for possible change in parameters of statistical distributions occuring at unknown time point, Ann. Math. Statist. 37 (1966) 1196-1210. doi: 10.1214/aoms/1177699265
  • [7] D. Kim, A Bayesian significance test of the stationarity of regression parametres, Biometrika 78 (1991) 667-675. doi: 10.2307/2337036
  • [8] D.V. Hinkley, Inference about the change-point in a sequence of random variables, Biometrika 57 (1970) 1-17. doi: 10.2307/2334932
  • [9] E.S. Page, Continuous inspection schemes, Biometrika 41 (1954) 100-115.
  • [10] E.S. Page, A test for change in a parameter occurring at an unknown point, Biometrika 42 (1955) 523-527. doi: 10.2307/2333009
  • [11] A. Sen and M.S. Srivastava, Some one-sided tests for change in level, Technometrics 17 (1975) 61-64. doi: 10.2307/1268001
  • [12] D. Siegmund, Boundary Crossing probabilities and statistical applications, Ann. Statist. 14 (1986) 361-404. doi: 10.1214/aos/1176349928
  • [13] D. Siegmund, Confidence sets in change point problem, Int. Statist. Rev. 56 (1988) 31-48. doi: 10.2307/1403360
  • [14] K.J. Worsley, The power of likelihood ratio and cumulative sum tests for a change in a binomial probability, Biometrika 70 (1983) 455-464. doi: 10.2307/2335560
  • [15] K.J. Worsley, Confidence regions and tests for a change-point in a sequence of exponential family random variables, Biometrika 73 (1986) 91-104. doi: 10.2307/2336275
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1169
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