Research Article

Bu çalışmada, Normal dağılımlı raslantı değişkenlerinin ortalaması ve varyansında değişme noktasının gözlenmesi problemi ele alınmıştır. Değişme noktasının yerinin tahmini için Bayesci yöntem kullanılmış ve parametrelerin bilgi içermeyen ve bilgi içeren önsel dağılımlı olması varsayımı altında değişme noktasının marjinal sonsal dağılımı elde edilmiştir. Değişme noktasının tahmini üzerinde önsel dağılımların performansları geniş benzetim çalışması ile farklı örneklem büyükleri için araştırılmıştır.

- [1] J.M. Bernardo, Noninformative priors do not exist: a discussion with José M. Bernardo, J. Statist. Planning and Inference 65 (1997), pp. 159-189 (to appear, with discussion)
- [2] J.M. Bernardo, E. Gutierrcz-Pefia and A.F.M. Smith, Comment to 'Exponential and Bayesian conjugate families: review and extensions', Test 6 (1997), pp. 70-71.
- [3] H. Boudjellaba, B. MacGibbon, P. Sawyer, On exact inference for change in a Poisson Sequence, Communications in Statistics A: Theory and Methods 30(3) (2001), pp. 407434.
- [4] J. Chen, A.K. Gupta, Testing and locating variance change points with application to stock prices, Journal of the American Statistical Association: JASA 92(438) (1997), pp.739-747.
- [5] J. Chen, A.K. Gupta, Change point analysis of a Gaussian mode, Statistical Papers 40 (1999), pp. 323–333.
- [6] J. Chen, A.K. Gupta, On change point detection and estimation, Communications in Statistics-Simulation and Computation 30 (2001), pp. 665-697.
- [7] J. Chen, A.K. Gupta, Statistical inference of covariance change points in Gaussian model, Statistics 38 (2004), pp. 17-28.
- [8] J. Chen, A.K. Gupta, A Bayesian approach to the statistical analysis of a smooth–abrupt change point analysis, Advances and Applications in Statistics 7 (2007), pp. 115-125.
- [9] D. Ghorbanzadeh, R. Lounes, Bayesian analysis for detecting a change in exponential family, Applied Mathematics and Computation 124 (2001), pp. 1-15.
- [10] A.K. Gupta, J. Chen, Detecting changes of mean in multidimensional normal sequences with application to literature and geology, Computational Statistics 11 (1996), pp. 211-221.
- [11] P. Haccou, E. Meelis, S. Geer, The likelihood ratio test for the change point problem for exponentially distributed random variables, Stochastic Process and Their Applications 27 (1988), pp. 121-139.
- [12] D.V. Hinkley, Inference about the change-point in a sequence of random variables, Biometrika 57(1) (1970), pp. 1-17.
- [13] D.V. Hinkley, E.A. Hinkley, Inference about the chance-point in a sequence of binomial variables, Biometrika 57(3) (1970), pp. 477-488.
- [14] D.A. Hsu, Detecting shifts of parameter Gamma sequences with applications to stock price and air traffic flow analysis, Journal of the American Statistical Association JASA 74 (1979), pp. 31-40.
- [15] B.H. Lavenda, Derivation of the prior distribution in Bayesian analysis from the principle of statistical equivalence, Open Sys. & Information Dyn. 8 (2001), pp. 103-114.
- [16] U. Menzefricke, A Bayesian Analysis of a Jump in the Precision of a Sequence of Independent Normal Random Variables at an Unknown Time Point, Applied Statistics 30 (1981), pp. 141-146.
- [17] E.S. Page, A test for a change in a parameter occurring at an unknown point, Biometrika 42 (1955), pp. 523-527.
- [18] A.F.M. Smith, A Bayesian approach to inference about a change point in a sequence of random variables, Biometrika 62 (1975), pp. 407-416.
- [19] K.J. Worsley, On the likelihood ratio test for a shift in location of normal populations, Journal of the American Statistical Association JASA 74 (1979), pp. 365-367.
- [20] K.J. Worsley, Confidence region and test for a change-point in a sequence of exponential family random variables, Biometrika 73(1) (1986), pp. 91-104.
- [21] Q. Yao, Tests for change-points with epidemic alternatives, Biometrika 80 (1993), pp. 179-191.

In this paper, the problem of one change point occurring simultaneously in both the mean and variance of a sequence of normal random variables is considered. The Bayesian method is used for the estimation of change point location; and the marginal posterior distributions of the change point location are obtained under the assumptions of noninformative and informative prior distributions for the parameters. The performances of the prior distributions on the estimation of the change point location, with different sample sizes, are investigated via extensive simulation studies.

- [1] J.M. Bernardo, Noninformative priors do not exist: a discussion with José M. Bernardo, J. Statist. Planning and Inference 65 (1997), pp. 159-189 (to appear, with discussion)
- [2] J.M. Bernardo, E. Gutierrcz-Pefia and A.F.M. Smith, Comment to 'Exponential and Bayesian conjugate families: review and extensions', Test 6 (1997), pp. 70-71.
- [3] H. Boudjellaba, B. MacGibbon, P. Sawyer, On exact inference for change in a Poisson Sequence, Communications in Statistics A: Theory and Methods 30(3) (2001), pp. 407434.
- [4] J. Chen, A.K. Gupta, Testing and locating variance change points with application to stock prices, Journal of the American Statistical Association: JASA 92(438) (1997), pp.739-747.
- [5] J. Chen, A.K. Gupta, Change point analysis of a Gaussian mode, Statistical Papers 40 (1999), pp. 323–333.
- [6] J. Chen, A.K. Gupta, On change point detection and estimation, Communications in Statistics-Simulation and Computation 30 (2001), pp. 665-697.
- [7] J. Chen, A.K. Gupta, Statistical inference of covariance change points in Gaussian model, Statistics 38 (2004), pp. 17-28.
- [8] J. Chen, A.K. Gupta, A Bayesian approach to the statistical analysis of a smooth–abrupt change point analysis, Advances and Applications in Statistics 7 (2007), pp. 115-125.
- [9] D. Ghorbanzadeh, R. Lounes, Bayesian analysis for detecting a change in exponential family, Applied Mathematics and Computation 124 (2001), pp. 1-15.
- [10] A.K. Gupta, J. Chen, Detecting changes of mean in multidimensional normal sequences with application to literature and geology, Computational Statistics 11 (1996), pp. 211-221.
- [11] P. Haccou, E. Meelis, S. Geer, The likelihood ratio test for the change point problem for exponentially distributed random variables, Stochastic Process and Their Applications 27 (1988), pp. 121-139.
- [12] D.V. Hinkley, Inference about the change-point in a sequence of random variables, Biometrika 57(1) (1970), pp. 1-17.
- [13] D.V. Hinkley, E.A. Hinkley, Inference about the chance-point in a sequence of binomial variables, Biometrika 57(3) (1970), pp. 477-488.
- [14] D.A. Hsu, Detecting shifts of parameter Gamma sequences with applications to stock price and air traffic flow analysis, Journal of the American Statistical Association JASA 74 (1979), pp. 31-40.
- [15] B.H. Lavenda, Derivation of the prior distribution in Bayesian analysis from the principle of statistical equivalence, Open Sys. & Information Dyn. 8 (2001), pp. 103-114.
- [16] U. Menzefricke, A Bayesian Analysis of a Jump in the Precision of a Sequence of Independent Normal Random Variables at an Unknown Time Point, Applied Statistics 30 (1981), pp. 141-146.
- [17] E.S. Page, A test for a change in a parameter occurring at an unknown point, Biometrika 42 (1955), pp. 523-527.
- [18] A.F.M. Smith, A Bayesian approach to inference about a change point in a sequence of random variables, Biometrika 62 (1975), pp. 407-416.
- [19] K.J. Worsley, On the likelihood ratio test for a shift in location of normal populations, Journal of the American Statistical Association JASA 74 (1979), pp. 365-367.
- [20] K.J. Worsley, Confidence region and test for a change-point in a sequence of exponential family random variables, Biometrika 73(1) (1986), pp. 91-104.
- [21] Q. Yao, Tests for change-points with epidemic alternatives, Biometrika 80 (1993), pp. 179-191.

There are 21 citations in total.

Primary Language | English |
---|---|

Journal Section | Articles |

Authors | |

Publication Date | December 30, 2017 |

Published in Issue | Year 2017 Volume: 10 Issue: 2 |