Classical and bayesian approaches to the change-point problem : fixed sample and sequential procedures

Zacks, S.

Zacks, S.

Statistique et analyse des données, Tome 7 (1982) no. 1, pp. 48-81.

MR Zbl | 2 citations dans Numdam

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     title = {Classical and bayesian approaches to the change-point problem : fixed sample and sequential procedures},
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     pages = {48--81},
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     volume = {7},
     number = {1},
     year = {1982},
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     zbl = {0511.62091},
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     url = {http://archive.numdam.org/item/SAD_1982__7_1_48_0/}
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Zacks, S. Classical and bayesian approaches to the change-point problem : fixed sample and sequential procedures. Statistique et analyse des données, Tome 7 (1982) no. 1, pp. 48-81. http://archive.numdam.org/item/SAD_1982__7_1_48_0/

Bibliographie
Cité par

[1] Bagshaw, M. and Johnson, R.A. (1975) The influence of reference values and estimated variance on the ARL of CUSUM tests. J.R.S.S., B, 37, 413-420. | MR | Zbl

[2] Bagshaw, M. and Johnson, R.A. (1975) Sequential detection of a drift change in a Wiener process. Commu. Statist. 4, 787-796. | MR | Zbl

[3] Bagshaw, M. and Johnson, R.A. (1975) The effect of serial correlation on the performance of CUSUM tests II. - Technometrics, 17, 73-80. | MR | Zbl

[4] Balmer, D.W. (1975) On a quickest detection problem with costly information. J. Appl. Prob., 12, 87-97. | MR | Zbl

[5] Balmer, D.W. (1981) On quickest detection problem with variable monitoring. J. Appl. Prob., 18, 760-767. | MR | Zbl

[6] Barnard, G.A. (1959) Control charts and stochastic processes. J. Roy. Statist. Soc. B, 21, 239-271. | Zbl

[7] Bather, J.A. (1967) On a quickest detection problem. Ann. Math. Statist., 38, 711-724. | MR | Zbl

[8] Bather, J.A. (1976) A control chart model and a generalized stopping problem for Brownian motion. Math. Oper. Res., 1, 209-224. | MR | Zbl

[9] Bhattacharyya, G.K. and Johnson, R.A. (1968) Non-parametric tests for shift at an unknown time point. Ann. Math. Statist., 39, 1731-1743. | MR | Zbl

[10] Broemeling, L. (1974) Estimating the future values of changing sequences. Commu. Statist., A, 6, 87-102. | Zbl

[11] Broemeling, L.D. (1974) Bayesian inferences about a changing sequence of random variables. Commun. Statist., 3, 234-255. | MR | Zbl

[12] Brown, R.L., Durbin, J. and Evans, J.M. (1975) Techniques for testing the constancy of regression relationships over time. J. Royal Statist. Soc, B 37, 149-192. | MR | Zbl

[13] Brown, R.L. and Durbin, J. (1968) Methods of investigating whether a regression relationship is constant over time. Selected Statistical Papers I. Amsterdam : Math. Centrum, European Meeting, 37-45. | Zbl

[14] Chernoff, H. and Zacks, S. (1964) Estimating the current mean of a normal distribution which is subjected to changes in time. Ann. Math. Statist., 35, 999-1028. | MR | Zbl

[15] Coob, G.W. (1978) The problem of the Nile : conditional solution to a change point problem. Biometrika, 62, 243-251. | Zbl

[16] Darkhovshk, B.S. (1976) A non-parametric method for the a posteriori detection of the "disorder" time of a sequence of independent random variables. Theory of Prob. Appl., 21, 178-183. | Zbl

[17] El-Sayyad, G.M. (1975) A Bayesian analysis of the change-point problem. Egypt. Statist.J., 19, 1-13.

[18] Farley, J.U. and Hinich, M.J. (1970) Detecting "small" mean shifts in time series. Management Science, 17, 189-199. | Zbl

[19] Ferriera, P.E. (1975) A Bayesian analysis of switching regression model: Known number of regimes. J. Amer. Statist. Assoc., 70, 370-374. | Zbl

[20] Fisz, M. (1963) Probability Theory and Mathematical Statistics. 3rd Edition. John Wiley and Sons, New-York. | MR | Zbl

[21] Gardner, L.A. Jr. (1969) On detecting changes in the mean of normal variates. Ann. Math. Statist., 40, 114-115. | MR | Zbl

[22] Girshick, M.A. and Rubin, H. (1952) A Bayes appoach to a quality control model. Ann. Math. Statist. 23, 114-115. | MR | Zbl

[23] Hawkins, D.M. (1977) Testing a sequence of observations for a shift in location. J. Amer. Statist. Assoc., 72, 180-186. | MR | Zbl

[24] Hawkins, D.M. (1980) A note on continuous and discontinuous segmented regression. Technometrics, 22, 443-444. | Zbl

[25] Hines, W.G.S. (1976) A simple monitor of a system with sudden parameter changes. IEEE Trans. Inf. Theory, IT, 210-216. | Zbl

[26] Hinkley, D.V. and Hinkley, E.A. (1970) Inference about the change-point in a sequence of Binomial random variables. Biometrika, 57, 477-488. | MR | Zbl

[27] Hinkley, D.V. (1969) Inference about the intersection in two-phase regression. Biometrika, 56, 495-504. | Zbl

[28] Hinkley, D.V. (1970) Inference about the change-point in a sequence of random variables. Biometrika, 57, 1-16. | MR | Zbl

[29] Hinkley, D.V. (1971) Inference in two phase regression. J. Amer. Statist. Assoc., 66, 736-743. | Zbl

[30] Hinkley, D.V. (1971) Inference about the change-point from a cumulative sum tests. Biometrika, 58, 509-523. | MR | Zbl

[31] Hinkley, D.V. (1972) Time-ordered classification. Biometrika, 59, 509-523. | MR | Zbl

[32] Holbert, D. and Broemeling, L. (1977) Bayesian inferences related to shifting sequences and two-hase regression. Commun. Statist. A, 6, 265-275. | MR | Zbl

[33] Hsu, D.A. (1977) Tests for variance shift at an unknown time point. Applied Statist., 26, 279-284.

[34] Hsu, D.A. (1979) Detecting shifts of parameter in Gamma sequences with applications to stock price and air traffic flow analysis. J. Amer. Statist. Asso., 74, 31-40.

[35] Inselmann, E.H. and Arsenal, F. (1968) Tests for several regression equations. Ann. Math. Statist., 39, 1362.

[36] Kander, A. and Zacks, S. (1966) Test procedures for possible changes in parameters of statistic at distributions occuring at unknown time points. Ann. Math. Statist., 37, 1196-1210. | MR | Zbl

[37] Khan, R.A. (1975) A sequential detection procedure. Tech. Rep. n° 17, Départ. of Statistics, CWRU.

[38] Khan, R.A. (1979) Some first passage problems related to CUSUM procedures. Stoch. Proc Appl., 9, 207-216. | MR | Zbl

[39] Lai, T.L. (1973) Gaussian processes, moving averages and quickest detection problems. Ann. Prob., 1, 825-837. | MR | Zbl

[40] Lai, T.L. (1974) Control charts based on weighted sums. Ann. Statist. 2, 134-147. | MR | Zbl

[41] Lee, A.F.S. and Heghinian, S.M. (1977) A shift of the mean level in a sequence of independent normal random variables - a Bayesian approach. Technometrics, 19, 503-506. | MR | Zbl

[42] Lorden, G. and Eisenberg, I. (1973) Detection of failure rate increases. Technometrics, 15, 167-175. | Zbl

[43] Lorden, G. (1971) Procedures for reacting to a change in distribution. Ann. Math. Statist., 42, 1897-1908. | MR | Zbl

[44] Maronna, R. and Yohai, V.J. (1978) A bivariate test for the dectection of a systematic change in mean. J. Amer. Statist. Assoc., 73, 640-645. | MR | Zbl

[45] Mustafi, C.K. (1968) Inference problems about parameters which are subjected to changes over time. Ann. Math. Statist., 39, 840-854. | MR | Zbl

[46] Nadler, J. and Robbins, N.D. (1971) Some characteristics of Page's two sided procedure for detecting a change in the location parameter. Ann. Math. Statist., 42, 538-551. | MR | Zbl

[47] Page, E.S. (1954) Continuous inspection schemes. Biometrika 41, 100-115. | MR | Zbl

[48] Page, E.S. (1955) A test for a change in a parameter occuring at an unknown point. Biometrika, 42, 523-526. | MR | Zbl

[49] Page, E.S. (1957) On problem in which a change in a parameter occurs at an unknown point. Biometrika, 44, 248-252. | Zbl

[50] Pettitt, A.N. (1979) A non parametric approach to the change-point problem. Appl. Statist., 28, 126-135. | MR | Zbl

[51] Quandt, R.E. (1958) The estimation of the parameters of a linear regression system obeys two separate regimes. J. Amer. Statis. Assoc. | MR | Zbl

[52] Quandt, R.E. (1960) Tests of the hypothesis that a linear regression System obeys two separate regimes. J. Amer. Statist. Assoc., 55, 324-330. | MR | Zbl

[53] Rao, P.S.E.S. (1972) On two phase regression estimator. Sankhya, 34, 473-476. | MR | Zbl

[54] Schweder, T. (1976) Some 'optimal' methods to detect structural shift or outliers in regression. J. Amer. Statist. Assoc., 71, 491-501. | MR | Zbl

[55] Sen, A. and Srivastave, M. (1975) On tests for detecting change in the mean when variance is unknown. Ann. Inst. Statist. Math., 27, 593-602. | MR | Zbl

[56] Sen, A. and Srivastava, M.S. (1975) On tests for detecting changes in means. Annals of Statist., 3, 98-108. | MR | Zbl

[57] Sen, A. and Srivastava, M.S. (1975) On one sided tests for change in level. Technometrics, 17, 61-64. | Zbl

[58] Sen, A.K. and Srivastava, M.S. (1973) On multivariate tests for detecting change in mean. Sankhya, 35, 173-186. | MR | Zbl

[59] Shaban, S.A. (1980) Change point problem and two-hase regression : an annotated bibliography. Inst. Statist. Review, 48, 83-93. | MR | Zbl

[60] Shiryaev, A.N. (1973) On optimum methods in quickest detection problems. Theory Prob. Appl., 8, 22-46. | Zbl

[61] Shiryaev, A.N. (1973) Statistical Sequential Analysis: Optimal Stopping Rules. Translations of Mathematical Monographs, Vol. 38, American Mathematical Society, Providence RI. | MR | Zbl

[62] Smith, A.F.M. (1975) A Bayesian approach to inference about change-point in sequence of random variables. Biometrika, 62, 407-43 6. | MR | Zbl

[63] Smith, A.F.M. (1977) A Bayesian analysis of some time varying models. Recent Developments in Statistics, J.R. Barra, et.al., Editors, North Holland, New York. | MR | Zbl

[64] Swamy, P.A.V.B. and Mehta, J.S. (1975) Bayesian and non-Bayesian analysis of switching regressions and of random coefficient regression. J. Amer. Statist. Assoc., 70, 593-602. | MR | Zbl

[65] Tsurumi, H. (1977) A Bayesian test of a parameter shift and an application. Jour. of Econometrics, 6, 371-380. | Zbl

[66] Von Mises, R. (1964) Mathematical Theory of Probability and Statistics Academic Press, New York. | MR | Zbl

[67] Whichern, D.W., Miller, R.B. and Hsu D.A. (1976) Change of variance in first-order autoregressive time series models with an application. Appl. Statist. 25, 248-256.

[68] Zacks, S. and Yadin, M. (1978) Adaptation of the service capacity in a queueing System which is subjected to a change in the arrival rate... Adv. Appl. Prob., 10, 666-681. | MR | Zbl

[69] Zacks, S. and Barzily, Z. (1981) Detecting a shift in the probability of success in a sequence of Bernouilli trials. J. Statist. Planning and Inf., 5, 107-119. | MR | Zbl

[70] Zacks, S. (1981) Parametric Statistical Inference : Basic Theory and Modern Approaches. Pergamon Press, Oxford. | MR | Zbl

[71] Zacks, S. (1981) The probability distribution and the expected value of a stopping variable associated with one-sided CUSUM procedures... Commum. Statist., A, 10, 2245-2258. | MR | Zbl