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Theory and Methods

Estimation of Knots in Linear Spline Models

, &
Pages 639-650 | Received 28 Apr 2020, Accepted 07 Jun 2021, Published online: 09 Aug 2021

References

  • Bacon, D. W., and Watts, D. G. (1971), “Estimating the Transition Between Two Intersecting Straight Lines,” Biometrika, 58, 525–534. DOI: 10.1093/biomet/58.3.525.
  • Bellman, R., and Roth, R. (1969), “Curve Fitting by Segmented Straight Lines,” Journal of the American Statistical Association, 64, 1079–1084. DOI: 10.1080/01621459.1969.10501038.
  • Carlin, B. P., Gelfand, A. E., and Smith, A. F. (1992), “Hierarchical Bayesian Analysis of Changepoint Problems,” Journal of the Royal Statistical Society, Series C, 41, 389–405. DOI: 10.2307/2347570.
  • Chen, C. W., Chan, J. S., Gerlach, R. and Hsieh, W. Y. (2011), “A Comparison of Estimators for Regression Models With Change Points,” Statistics and Computing, 21, 395–414. DOI: 10.1007/s11222-010-9177-0.
  • Chiu, G., Lockhart, R., and Routledge, R. (2002), “Bent-Cable Asymptotics When the Bend is Missing,” Statistics and Probability Letters, 59, 9–16. DOI: 10.1016/S0167-7152(02)00138-4.
  • Chiu, G., Lockhart, R., and Routledge, R. (2006), “Bent-Cable Regression Theory and Applications,” Journal of the American Statistical Association, 101, 542–553.
  • Cui, Y., Pang, J.-S. and Sen, B. (2018), “Composite Difference-Max Programs for Modern Statistical Estimation Problems,” SIAM Journal on Optimization, 28, 3344–3374. DOI: 10.1137/18M117337X.
  • Das, R., Banerjee, M., Nan, B., and Zheng, H. (2016), “Fast Estimation of Regression Parameters in a Broken-Stick Model for Longitudinal Data,” Journal of the American Statistical Association, 111, 1132–1143. DOI: 10.1080/01621459.2015.1073154.
  • De Somer, F., Mulholland, J. W., Bryan, M. R., Aloisio, T., Van Nooten, G. J. and Ranucci, M. (2011), “O2 Delivery and CO2 production during Cardiopulmonary Bypass as Determinants of Acute Kidney Injury: Time for a Goal-Directed Perfusion Management?,” Critical Care, 15, R192.
  • Elliott, M. R. and Shope, J. T. (2003), “Use of a Bayesian Changepoint Model to Estimate Effects of a Graduated Driver’s Licensing Program,” Journal of Data Science, 1, 43–63. DOI: 10.6339/JDS.2003.01(1).103.
  • Feder, P. I. (1975a), “The Log Likelihood Ratio in Segmented Regression,” The Annals of Statistics, 84–97. DOI: 10.1214/aos/1176343000.
  • Feder, P. I. (1975b), “On Asymptotic Distribution Theory in Segmented Regression Problems–Identified Case,” The Annals of Statistics, 3, 49–83. DOI: 10.1214/aos/1176342999.
  • Hudson, D. J. (1966), “Fitting Segmented Curves Whose Join Points Have to Be Estimated,” Journal of the American Statistical Association, 61, 1097–1129. DOI: 10.1080/01621459.1966.10482198.
  • Keller, M. B., McCullough, J. P., Klein, D. N., Arnow, B., Dunner, D. L., Gelenberg, A. J., Markowitz, J. C., Nemeroff, C. B., Russell, J. M., Thase, M. E. et al. (2000), “A Comparison of Nefazodone, the Cognitive Behavioral-Analysis System of Psychotherapy, and Their Combination for the Treatment of Chronic Depression,” New England Journal of Medicine, 342, 1462–1470. DOI: 10.1056/NEJM200005183422001.
  • Marsh, L. C., and Cormier, D. R. (2001), Spline Regression Models, Vol. 137, Thousand Oaks, CA: Sage.
  • Muggeo, V. M. (2003), “Estimating Regression Models with Unknown Break-Points,” Statistics in Medicine, 22, 3055–3071. DOI: 10.1002/sim.1545.
  • Muggeo, V. M. (2008), “Segmented: An r Package to Fit Regression Models With Broken-Line Relationships,” R News, 8, 20–25. Available at: https://cran.r-project.org/doc/Rnews/
  • Muggeo, V. M. (2016), “Testing With a Nuisance Parameter Present Only Under the Alternative: A Score-Based Approach With Application to Segmented Modelling,” Journal of Statistical Computation and Simulation, 86, 3059–3067. DOI: 10.1080/00949655.2016.1149855.
  • Qi, L., and Sun, J. (1993), “A Nonsmooth Version of Newton’s Method,” Mathematical Programming, 58, 353–367. DOI: 10.1007/BF01581275.
  • Quandt, R. E. (1958), “The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes,” Journal of the American Statistical Association, 53, 873–880. DOI: 10.1080/01621459.1958.10501484.
  • Ranucci, M., Romitti, F., Isgrò, G., Cotza, M., Brozzi, S., Boncilli, A., and Ditta, A. (2005), “Oxygen Delivery During Cardiopulmonary Bypass and Acute Renal Failure After Coronary Operations,” The Annals of Thoracic Surgery, 80, 2213–2220. DOI: 10.1016/j.athoracsur.2005.05.069.
  • Rigotti, T. (2009), “Enough is Enough? Threshold Models for the Relationship Between Psychological Contract Breach and Job-Related Attitudes,” European Journal of Work and Organizational Psychology, 18, 442–463. DOI: 10.1080/13594320802402039.
  • Smith, A., and Cook, D. (1980), “Straight Lines With a Change-Point: A Bayesian Analysis of Some Renal Transplant Data,” Journal of the Royal Statistical Society, Series C, 29, 180–189. DOI: 10.2307/2986304.
  • Tishler, A., and Zang, I. (1981), “A New Maximum Likelihood Algorithm for Piecewise Regression,” Journal of the American Statistical Association, 76, 980–987. DOI: 10.1080/01621459.1981.10477752.
  • Tsiatis, A. (2007), Semiparametric Theory and Missing Data, New York: Springer Science & Business Media.
  • van der Vaart, A. W. (2000), Asymptotic Statistics, Vol. 3. Cambridge: Cambridge University Press.
  • van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes: With Applications to Statistics, New York: Springer.

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