References
- Cole TJ, Freeman JV, Preece MA. British 1990 growth reference centiles for weight, height, body mass index and head circumference fitted by maximum penalized likelihood. Stat Med. 1998;17(4):407–429. doi: 10.1002/(SICI)1097-0258(19980228)17:4<407::AID-SIM742>3.0.CO;2-L
- Durbán M, Harezlak J, Wand MP, Carroll RJ. Simple fitting of subject-specific curves for longitudinal data. Stat Med. 2005;24(8):1153–1167. doi: 10.1002/sim.1991
- Ganger J, Brent M. Reexamining the vocabulary spurt. Dev Psychol. 2004;40(4):621–632. doi: 10.1037/0012-1649.40.4.621
- Flood SJ, Mitchell WJ, Oxnard CE, Turlach BA, McGeachie J. To evaluate the utility of smaller sample sizes when assessing dental maturity curves for forensic age estimation. J Forensic Sci. 2011;56(6):1604–1609. doi: 10.1111/j.1556-4029.2011.01884.x
- Firmin L, Müller S, Rösler KM. A method to measure the distribution of latencies of motor evoked potentials in man. Clin Neurophysiol. 2011;122(1):176–182. doi: 10.1016/j.clinph.2010.05.034
- Firmin L, Müller S, Rösler KM. The latency distribution of motor evoked potentials in patients with multiple sclerosis. Clin Neurophysiol. 2012;123(12):2414–2421. doi: 10.1016/j.clinph.2012.05.008
- Ratkowsky DA. Handbook of nonlinear regression models. New York: Marcel Dekker; 1990.
- Mirman D. Growth curve analysis and visualization using r. The R series. Boca Raton: Chapman & Hall/CRC; 2014.
- Panik JM. Growth curve modeling: theory and applications. Hoboken: John Wiley & Sons; 2014.
- Turlach BA. Shape constrained smoothing using smoothing splines. Comput Statist. 2005;20(1):81–103. doi: 10.1007/BF02736124
- Hazelton ML, Turlach BA. Semiparametric regression with shape constrained penalized splines. Comput Statist Data Anal. 2011;55(10):2871–2879. doi: 10.1016/j.csda.2011.04.018
- Meyer MC. Inference using shape-restricted regression splines. Ann Appl Stat. 2008;2(3):1013–1033. doi: 10.1214/08-AOAS167
- Meyer MC. Constrained penalized splines. Canad J Statist. 2012;40(1):190–206. doi: 10.1002/cjs.10137
- Marron JS, Turlach BA, Wand MP. Local polynomial smoothing under qualitative constraints. In: Billard L, Fisher NI, editors. Graph-image-vision; computing science and statistics; Vol. 28. Fairfax Station, VA 22039–7460: Interface Foundation of North America, Inc.; 1997. p. 647–652.
- Mammen E, Marron JS, Turlach BA, Wand MP. A general projection framework for constrained smoothing. Statist Sci. 2001;16(3):232–248. doi: 10.1214/ss/1009213727
- Friedman JH, Tibshirani R. The monotone smoothing of scatterplots. Technometrics. 1984;26(3):243–250. doi: 10.1080/00401706.1984.10487961
- Mammen E. Estimating a smooth monotone regression function. Ann Statist. 1991;19(2):724–740. doi: 10.1214/aos/1176348117
- Hall P, Huang LS. Nonparametric kernel regression subject to monotonicity constraints. Ann Statist. 2001;29(3):624–647. doi: 10.1214/aos/1009210683
- Dette H, Neumeyer N, Pilz KF. A simple nonparametric estimator of a strictly monotone regression function. Bernoulli. 2006;12(3):469–490. doi: 10.3150/bj/1151525131
- Dette H, Pilz KF. A comparative study of monotone nonparametric kernel estimates. J Stat Comput Simul. 2006;76(1):41–56. doi: 10.1080/00949650412331321061
- Ramsay JO. Estimating smooth monotone functions. J R Stat Soc Ser B. 1998;60(2):365–375. doi: 10.1111/1467-9868.00130
- Murray K, Müller S, Turlach BA. Revisiting fitting monotone polynomials to data. Comput Statist. 2013;28(5):1989–2005. doi: 10.1007/s00180-012-0390-5
- Elphinstone CD. A target distribution model for non-parametric density estimation. Comm Statist Theory Methods. 1983;12(2):161–198. doi: 10.1080/03610928308828450
- Hawkins DM. Fitting monotonic polynomials to data. Comput Statist. 1994;9(3):233–247.
- Hall P. The bootstrap and edgeworth expansion. New York: Springer-Verlag; 1992.
- Efron B, Tibshirani RJ. An introduction to the bootstrap. Monographs on statistics and applied probability, Vol. 57. London: Chapman and Hall; 1993.
- Hjorth JSU. Computer intensive statistical methods: validation, model selection and bootstrap. London: Chapman and Hall; 1994.
- Shao J, Tu D. The jackknife and bootstrap. Springer series in statistics. New York: Springer-Verlag; 1995.
- Davison AC, Hinkley DV. Bootstrap methods and their application. Cambridge Series in Statistical and Probabilistic Mathematics, Vol. 1. Cambridge: Cambridge University Press; 1997.
- Lunneborg CE. Data analysis by resampling: concepts and applications. Pacific Grove (CA): Duxbury Press; 2000.
- Hall P, Horowitz J. A simple bootstrap method of constructing nonparametric confidence bands for functions. Ann Statist. 2013;41(1):1982–1921.
- Dümbgen L. Optimal confidence bands for shape-restricted curves. Bernoulli. 2003;9(3):423–449. doi: 10.3150/bj/1065444812
- Strand M, Zhang Y, Swihart B. Monotone nonparametric regression and confidence intervals. Comm Statist Simulation Comput. 2010;39:828–845. doi: 10.1080/03610911003650367
- Karlin S, Studden WJ. Tchebycheff systems: with applications in analysis and statistics. New York: Wiley & Sons; 1966.
- Dette H, Studden WJ. The theory of canonical moments with applications in statistics, probability, and analysis. Wiley series in probability and statistics. New York: Wiley & Sons; 1997.
- Brickman L, Steinberg L. On nonnegative polynomials. Amer Math Monthly. 1962;69(3):218–221. doi: 10.2307/2311058
- Fausett LV. Numerical methods: algorithms and applications. Upper Saddle River (NJ): Prentice Hall; 2003.
- Osborne MR. Nonlinear least squares – the Levenberg algorithm revisited. J Aust Math Soc. 1976;19(3):343–357. doi: 10.1017/S033427000000120X
- Murray K. Improved monotone polynomial fitting with applications and variable selection [PhD thesis]. Sydney, NSW, Australia: The University of Sydney; 2015.
- Shevchuk IA. Approximation of monotone functions by monotone polynomials. Russ Acad Sci Sb Math. 1993;76(1):51–64. doi:10.1070/SM1993v076n01ABEH003401.
- Heinzmann D. A filtered polynomial approach to density estimation. Comput Statist. 2008;23(3):343–360. doi: 10.1007/s00180-007-0070-z
- Barlow RE, Bartholomew DJ, Bremner JM, Brunk HD. Statistical inference under order restrictions. London: John Wiley & Sons; 1972.
- Silvapulle MJ, Sen PK. Constrained statistical inference: inequality, order and shape restrictions. Wiley series in probability and statistics. Hoboken (NJ): John Wiley & Sons; 2005.
- Shao J. Bootstrap model selection. J Amer Statist Assoc. 1996;91(434):655–665. doi: 10.1080/01621459.1996.10476934
- Shao J. Bootstrap sample size in non-regular cases. Proc Amer Math Soc. 1994;122(4):1251–1262. doi: 10.1090/S0002-9939-1994-1227529-8
- Stine RA. Bootstrap prediction intervals for regression. J Amer Statist Assoc. 1985;80(392):1026–1031. doi: 10.1080/01621459.1985.10478220
- Müller S, Welsh A. Outlier robust model selection in linear regression. J Amer Statist Assoc. 2005;100(472):1297–1310. doi: 10.1198/016214505000000529
- Müller S, Welsh AH. Robust model selection in generalized linear models. Statist Sinica. 2009;19(3):1155–1170.
- Demirjian A, Goldstein H, Tanner JM. New system of dental age assessment. Hum Biol. 1973;45(2):211–227.
- Chaillet N, Nystrom M, Kataja M, Demirjian A. Dental maturity curves in finnish children: Demirjian's method revisited and polynomial functions for age estimation. J Forensic Sci. 2004;49(6):1324–1331. doi: 10.1520/JFS2004211
- R Core Team. R: a language and environment for statistical computing. R Foundation for Statistical Computing; Vienna, Austria; 2015. Available from: http://www.R-project.org/.