References
- Bai, J., and P. Perron. 1998. Estimating and testing linear models with multiple structural changes. Econometrics 70:9–38.
- Bai, J., and P. Perron. 2003. Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18 (1):1–22. doi:https://doi.org/10.1002/jae.659.
- Brodsky, B. E., and B. S. Darkhovsky. 1993. Nonparametric methods in change-point problems. Dordrecht: Kluwer Academic Publishers Group.
- Chen, C. W. S., J. S. K. Chan, R. H. Gerlach, and W. Y. L. Hsieh. 2011. A comparison of estimators for regression models with change points. Statistics and Computing 21 (3):395–414. doi:https://doi.org/10.1007/s11222-010-9177-0.
- Chen, H.-S., S. Zeichner, R. N. Anderson, D. Espey, H.-J. Kim, and E. J. Feuer. 2020. The joinpoint-jump and joinpoint-comparability ratio model for trend analysis. Journal of Official Statistics, to Appear. Advanced online publication.
- Chen, J., and A. K. Gupta. 2000. Parametric Statistical Change Point Analysis. Boston: Birkhäuser.
- Chiu, G., R. Lockhart, and R. Routledge. 2002. Bent-cable asymptotics when the bend is missing. Statistics & Probability Letters 59 (1):9–16. doi:https://doi.org/10.1016/S0167-7152(02)00138-4.
- Chiu, G., R. Lockhart, and R. Routledge. 2006. Asymptotic theory for bent-cable regression: The basic bent-cable regression theory and applications. Journal of the American Statistical Association 101 (474):542–53. doi:https://doi.org/10.1198/016214505000001177.
- Chow, G. C. 1960. Tests of equality between sets of coefficients in two linear regressions. Econometrica 28 (3):591–605. doi:https://doi.org/10.2307/1910133.
- Csörgő, M., and L. Horváth. 1997. Limit theorems in change-point analysis. New York: John Wiley & Sons.
- Feder, P. 1975. On asymptotic distribution theory in segmented regression problems-identified case. The Annals of Statistics 3 (1):49–83. doi:https://doi.org/10.1214/aos/1176342999.
- Hawkins, D. M. 2001. Fitting multiple change-point models to data. Computational Statistics & Data Analysis 37:323–41. doi:https://doi.org/10.1016/S0167-9473(00)00068-2.
- Hinkley, D. V. 1969. Inference about the intersection in two-phase regression. Biometrika 56 (3):495–504. doi:https://doi.org/10.1093/biomet/56.3.495.
- Hinkley, D. V. 1971. Inference in two-phase regression. Journal of the American Statistical Association 66 (336):736–43. doi:https://doi.org/10.1080/01621459.1971.10482337.
- Horváth, L., M. Hušková, and M. Serbinowska. 1997. Estimators for the time of change in linear models. Statistics 29 (2):109–30. doi:https://doi.org/10.1080/02331889708802578.
- Hudson, D. 1966. Fitting segmented curves whose join points have to be estimated. Journal of the American Statistical Association 61 (316):1097–129. doi:https://doi.org/10.1080/01621459.1966.10482198.
- Jarušková, D. 2003. Asymptotic distribution of a statistic testing a change in simple linear regression with equidistant design. Statistics & Probability Letters 64 (1):89–95. doi:https://doi.org/10.1016/S0167-7152(03)00143-3.
- Julious, S. A. 2001. Inference and estimation in a changepoint regression problem. Journal of the Royal Statistical Society: Series D (The Statistician) 50 (1):51–61. doi:https://doi.org/10.1111/1467-9884.00260.
- Khodadadi, A., and M. Asgharian. 2008. Change-point problems and regression: An annotated bibliography. Collection of Biostatistics Research Archive (COBRA) Preprint series 2008; Working Paper 44 (http://biostats.bepress.com/cobra/art44).
- Kim, H.-J., B. Yu, and E. J. Feuer. 2008. Inference in segmented line regression: A simulation study. Journal of Statistical Computation and Simulation 78 (11):1087–103. doi:https://doi.org/10.1080/00949650701528461.
- Kim, H.-J., B. Yu, and E. J. Feuer. 2009. Selecting the number of change-points in segmented line regression. Statistica Sinica 19 (2):597–609.
- Kim, H.-J., and D. Siegmund. 1989. The likelihood ratio test for a change-point in simple linear regression. Biometrika 76 (3):409–23. doi:https://doi.org/10.1093/biomet/76.3.409.
- Kim, H.-J., J. Luo, H.-S. Chen, D. Green, D. Buckman, J. Byrne, and E. J. Feuer. 2017. Improved confidence interval for average annual percent change in trend analysis. Statistics in Medicine 36 (19):3059–74. doi:https://doi.org/10.1002/sim.7344.
- Kim, H.-J., J. Luo, J. Kim, H.-S. Chen, and E. J. Feuer. 2014. Clustering of trend data using joinpoint regression models. Statistics in Medicine 33 (23):4087–103. doi:https://doi.org/10.1002/sim.6221.
- Kim, H.-J., M. Fay, E. J. Feuer, and D. N. Midthune. 2000. Permutation tests for joinpoint regression with applications to cancer rates. Statistics in Medicine 19 (3):335–51. (Correction: 2001. Statistics in Medicine 20: 655) doi:https://doi.org/10.1002/(SICI)1097-0258(20000215)19:3<335::AID-SIM336>3.0.CO;2-Z.
- Kim, J., and H.-J. Kim. 2008. Asymptotic results in segmented multiple regression. Journal of Multivariate Analysis 99 (9):2016–38. doi:https://doi.org/10.1016/j.jmva.2008.02.028.
- Kim, J., and H.-J. Kim. 2017. Corrigendum to “Asymptotic results in segmented multiple regression” [J. Multivariate Anal. 99 (2008) 2016-2038]. Journal of Multivariate Analysis 159:134–7.
- Koul, H. L., and L. Qian. 2002. Asymptotics of maximum likelihood estimator in a two-phase linear regression model. Journal of Statistical Planning and Inference 108 (1-2):99–119. doi:https://doi.org/10.1016/S0378-3758(02)00273-2.
- Lerman, P. M. 1980. Fitting segmented regression models by grid search. Applied Statistics 29 (1):77–84. doi:https://doi.org/10.2307/2346413.
- Liu, J., S. Wu, and J. V. Zidek. 1997. On segmented multivariate regression. Statistica Sinica 7:497–525.
- Muggeo, V. M. R. 2003. Estimating regression models with unknown break-points. Statistics in Medicine 22 (19):3055–71. doi:https://doi.org/10.1002/sim.1545.
- Muggeo, V. M. R. 2008. Segmented: An R package to fit regression models with broken-line relationships. R News 8:20–5.
- Muggeo, V. M. R. 2017. Interval estimation for the breakpoint in segmented regression: A smoothed score-based approach. Australian & New Zealand Journal of Statistics 59:311–22. doi:https://doi.org/10.1111/anzs.12200.
- Seber, G. A. F., and C. J. Wild. 1989. Nonlinear regression. Chichester, New York: John Wiley & Sons.
- Siegmund, D. O., and H. Zhang. 1994. Confidence regions in broken line regression. Change-point Problems. IMS Lecture Notes - Monograph Series 23:292–316.
- Tiwari, R. C., K. A. Cronin, W. Davis, E. J. Feuer, B. Yu, and S. Chib. 2005. Bayesian model selection for join point regression with application to age-adjusted cancer rates. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54:919–39. doi:https://doi.org/10.1111/j.1467-9876.2005.00518.x.
- Worsley, K. J. 1983. Testing for a two-phase multiple regression. Technometrics 25 (1):35–42. doi:https://doi.org/10.1080/00401706.1983.10487817.
- Yu, B., M. Barrett, H.-J. Kim, and E. J. Feuer. 2007. Estimating joinpoints in continuous time scale for multiple change-point models. Computational Statistics and Data Analysis 51 (5):2420–7. doi:https://doi.org/10.1016/j.csda.2006.07.044.