Two-phase_Change-point_Models.pdf

© 2009, Timothy G. Gregoire, Yale University

Last revised: November 2009

Two-phase, Switching, Change-point regressions and Mixture Models (51 entries) 1. Quandt, R.E. 1958. The estimation of the parameters of a linear regression system obeying two separate regimes. JASA: 873 – 880 2. Quandt, R.E. 1960. Tests of the hypothesis that a linear regression system obeys two separate regimes. JASA: 324 – 330 3. Sprent, P. 1961. Some hypothesis concerning two-phase regression lines. Biometrics 7: 634 – 645 4. Robinson, D.E. 1964. Estimates for the points of intersection of two polynomial regressions. American Statistical Association Journal: 214 – 224 5. Hudson, D.J. 1966. Fitting segmented curves whose join points have to be estimated. JASA (61): 1097 – 1129 6. Hinkley, D.V. 1969. Inference about the intersection in two-phase regression. Biometrika 56(3): 495 – 504 7. Bacon, D.W. 1971. Estimating the transition between two intersecting straight lines. Biometrika 58(3): 525 – 534 8. Hinkley, D.V. 1971. Inference in two-phase regression. Journal of the American Statistical Association 66(336): 736 – 743 9. Quandt, R.E. 1972. A new approach to estimating switching regressions. Journal of the American Statistical Association 67(338): 306 – 310 10. Gallant, A.R. and Fuller, W.A. 1973. Fitting segmented polynomial regression models whose join points have to be estimated. Journal of the American Statistical Association 68(341): 144 – 147 11. Watts, D.G. and Bacon, D.W. 1974. Using an hyperbola as a transition model to fit two-regime straight –line data. Technometrics 16(3): 369 – 373 12. Feder, P.I. 1975. On asymptotic distribution theory in segmented regression problems identified case. The Annals of Statistics 3(1): 49 – 83 13. Feder, P.I. 1975. The log likelihood ratio in segmented regression. The Annals of Statistics 3(1): 84 – 97

© 2009 Timothy G. Gregoire

Two-phase_Change-point_Models.pdf

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14. Swamy, P.A.V.B. and Mehta, J.S. 1975. Bayesian and Non-Bayesian analysis of switching regressions and of random coefficient regression models. JASA 70(351): 593 – 602 15. Titterington, D.M. 1976. Updating a diagnostic system using unconfirmed cases. Appl. Statist. 25(3): 238 – 247 16. Kiefer, N.M. 1978. Discrete parameter variation: Efficient estimation of a switching regression model. Econometrica 46(2): 427 – 434 17. Quandt, R.E. and Ramsey, J.B. 1978. Estimating mixtures of normal distributions aand switching regressions. JASA 73(364): 730 – 18. Beckman, R.J. and Cook, R.D. 1979. Testing for two-phase regressions. Technometrics 21(1): 65 – 69 19. Aitkin, M. and Wilson, G.T. 1980. Mixture models, outliers, and the EM Algorithm. Technometrics 22(3): 325 – 331 20. Binkley, C.S. and Miller, R.S. 1980. Survivorship of the whooping crane, Grus Americana. Ecology 61(2): 434 - 437 21. Binkley, C.S. and Miller, R.S. 1980. Population characteristics of the whooping crane Grus Americana. 22. Shaban, S.A. 1980. Change point problem and two-phase regression: an Annotated Bibliography. International Statistical Review 48: 83- 93. 23. Hinkley & T. Gregoire Corresp. 1983. Correspondence on two-phase regression. 24. Jones, R. and Molitoris, B.A. 1984. A statistical method for determining the breakpoint of two lines. Analytical Biochemistry 141: 287 – 290 25. Chappell, R. 1989. Fitting bent lines to data, with applications to allometry. J. theor. Boil. 138: 235 – 256 26. Kim, H. and Segmund, D. 1989. The Likelihood ratio test for a change-point in simple linear regression. Biometrika 76(3): 409 – 423 27. Titterington, D.M. 1990. Some recent research in the analysis of mixture distributions. Statistics 21(4): 619 – 641 28. Jones, R. H. and Dey, I. 1995. Determining one or more change points. Chemistry and Physics of Lipids 76: 1 – 6

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29. Kuchenhoff, H. and Carroll, R.J. 1995. Segmented regression with errors in predictors: semiparametric and parametric methods. 30. Aitkin, M. and Aitkin, I. 1996. A hybrid EM/Gauss-Newton algorithm for maximum likelihood in mixture distributions. Statistics and Computing 6: 127 130 31. Feng, Z.D. and McCulloch, C.E. 1996. Using bootstrap likelihood ratios in finite mixture models. Journal of the Royal Statistical Society 58(3): 609 – 617 32. Van Norden, S. and Vigfusson, R. 1996. Regime-switching models: A guide to the Bank of Canada Gauss Procedures. Working Paper 96-3. 33. Schroder, U. and Sondgerath, D. 1996. The concept of biological time for computing the switching points of a growth model for winter wheat. Ecological Modelling 88: 1- 8 34. Young, D.A. and Zamudio, S. 199? Breakpoint determination for repeated measures data using a nonlinear stochastic parameter model. 35. Titterington, D.M. 1997. Mixture Distribution (Update). Encyclopedia of Statistical Sciences: Update Volume 1. John Wiley & Sons, Inc. 36. Courbet, F. 1999. A three-segmented model for the vertical distribution of annual ring area: Application to Cedrus atlantica Menetti. Forest Ecology and Management 119: 177 – 194 37. Jeffries, N. and Pfeiffer, R. 2000. A mixture model for the probability distribution of rain rate. Environmetrics 12: 1- 10 38. Turner, T.R. 2000. Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions. Appl. Statist. 49(3): 371 - 384 39. Liu, C., Zhang, L., Davis, C.J., Solomon, D.S., and Gove, J.H. 2001. A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands. Can. J. For. Res. 31: 1654 – 1659 40. Liu, C., Zhang, L., Davis, C.J., Solomon, D.S., and Gove, J.H. 2002. A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. Forest Science 48(4): 653 – 661 41. Krieger, A.M., Pollak, M., and Yakir, B. 2003. Surveillance of a simple linear regression. Journal of the American Statistical Association 98(462): 456 – 42. Muggeo, V.M.R. 2003. Estimating regression models with unknown break-points. Statistics in Medicine 22: 3055 – 3071

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Two-phase_Change-point_Models.pdf

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43. Wright, D.E. and Bray, I. 2003. A mixture model for rounded data. The Statistician 52(1): 3-13 44. Chung, H., Loken, E., and Schafer, J.L. 2004. Difficulties in drawing inferences with finite-mixture models: A simple example with a simple solution. The American Statistician 58(2): 152 – 158 45. Gijbels, I. and Goderniaux, A. 2004. Bandwith selection for changepoint estimation in nonparametric regression. Technometrics 46(1): 76 – 86 46. Kim, H., Fay, M.P., Yu, B., Barrett, M.J., and Feuer, E.J. 2004. Compatibility of segmented line regression models. Biometrics 60: 1005 – 1014 47. Hall, D.B. and Wang, L. 2005. Two-component mixtures of generalized linear mixed effects models for cluster correlated data. Statistical Modelling 5: 21 – 37 48. Chiu, G., Lockhart, R., and Routledge, R. 2006. Bent-cable regression theory and applications. Journal of the American Statistical Association 101(474): 542 – 49. Jandhyala, V.K. and Fotopoulos, S.B. 2007. Estimating the unknown change point in the parameters of the lognormal distribution. Environmetrics 18: 141 – 155 50. Muggeo, V.M.R. 2008. Modeling temperature effects on mortality: multiple segmented relationships with common break points. Biostatistics: 1- 8 51. Muggeo, V.M.R., Attanasio, M. and Porcu, M. 2009. A segmented regression model for event history data: an application to the fertility patterns in Italy. Journal of Applied Statistics 36(9): 973 – 988

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