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Articles

Time-varying coefficient model estimation through radial basis functions

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Pages 2510-2534 | Received 13 Jul 2020, Accepted 25 Mar 2021, Published online: 05 Apr 2021

References

  • Y. Andriyana, I. Gijbels, and A. Verhasselt, Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity, Stat. Papers 59 (2018), pp. 1589–1621.
  • R.M. Assuncao, Space varying coefficient models for small area data, Environ. Off. J. Int. Environ. Soc. 14 (2003), pp. 453–473.
  • C. Biller and L. Fahrmeir, Bayesian varying-coefficient models using adaptive regression splines, Stat. Modelling. 1 (2001), pp. 195–211.
  • M.D. Buhmann, Radial Basis Functions, Cambridge University Press, 2004.
  • Z. Cai, J. Fan, and R. Li, Efficient estimation and inferences for varying-coefficient models, J. Am. Stat. Assoc. 95 (2000), pp. 888–902.
  • C.T. Chiang, J.A. Rice, and C.O. Wu, Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables, J. Am. Stat. Assoc. 96 (2001), pp. 605–619.
  • J.M. Chiou, Y. Ma, and C.L. Tsai, Functional random effect time-varying coefficient model for longitudinal data, Stat 1 (2012), pp. 75–89.
  • W.S. Cleveland, E. Grosse, and W.M. Shyu, Local regression models. statistical models in s (Chambers, J.M. and Hastie, T.J., Eds), 309–376. Wadsworth & Brooks, Pacific Grove, 1991,
  • E. Connick, M.M. Lederman, B.L. Kotzin, J. Spritzler, D.R. Kuritzkes, A.D. Sevin, L. Fox, M.H. Chiozzi, J.M. Leonard, F. Rousseau, J.D. Roe, A. Martinez, H. Kessler, and A. Landay, Immune reconstitution in the first year of potent antiretroviral therapy and its relationship to virologic response, J. Infect. Dis. 181 (2000), pp. 358–363.
  • B. Efron and T Hastie, Computer Age Statistical Inference, Vol. 5, Cambridge University Press, 2016.
  • R.L. Eubank, C. Huang, Y.M. Maldonado, N. Wang, S. Wang, and R.J. Buchanan, Smoothing spline estimation in varying-Coefficient models, J. R. Stat. Soc. Seri. B Stat. Method.) 66 (2004), pp. 653–667.
  • J. Fan and T. Huang, Profile likelihood inferences on semiparametric varying-coefficient partially linear models, Bernoulli 11 (2005), pp. 1031–1057.
  • J. Fan, Q. Yao, and Z. Cai, Adaptive varying-coefficient linear models, J. R. Stat. Soc.: Series B (Stat. Method.) 65 (2003), pp. 57–80.
  • J. Fan and J.T. Zhang, Two-step estimation of functional linear models with applications to longitudinal data, J. R. Stat. Soc.: Seri. B (Stat. Method.) 62 (2000), pp. 303–322.
  • J. Fan and W. Zhang, Statistical estimation in varying coefficient models, Annal. Stat. 27 (1999), pp. 1491–1518.
  • J. Fan and W. Zhang, Statistical methods with varying coefficient models, Stat. Interface. 1 (2008), pp. 179.
  • J.J. Faraway, Linear Models with R, CRC press, 2014.
  • M.A. Fischl, H.J. Ribaudo, A.C. Collier, A. Erice, M. Giuliano, M. Dehlinger, Jr. Eron, S.M. Hammer, S. Vella, G.D. Morse, and J.E. Feinberg, A randomized trial of 2 different 4-drug antiretroviral regimens versus a 3-drug regimen, in advanced human immunodeficiency virus disease, J. Infect. Dis. 188 (2003), pp. 625–634.
  • M. Franco-Villoria, M. Ventrucci, and H. Rue, A unified view on bayesian varying coefficient models, Electron. J. Stat. 13 (2019), pp. 5334–5359.
  • A.E. Gelfand, H.J. Kim, C.F. Sirmans, and S. Banerjee, Spatial modeling with spatially varying coefficient processes, J. Am. Stat. Assoc. 98 (2003), pp. 387–396.
  • A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin, Bayesian Data Analysis, CRC press, 2013.
  • A. Gelman and D. Rubin, Inferences from iterative simulation using multiple sequences, Stat. Sci. 7 (1992), pp. 457–472.
  • J. Harezlak, D. Ruppert, and M.P. Wand, Semiparametric Regression with R, Springer, 2018.
  • T. Hastie and R. Tibshirani, Varying-coefficient models, J. R. Stat. Soc.: Seri. B (Method.) 55 (1993), pp. 757–779.
  • T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Science & Business Media, 2009.
  • P.D. Hoff, A First Course in Bayesian Statistical Methods, Vol. 580, Springer, 2009.
  • D.R. Hoover, J.A. Rice, C.O. Wu, and L.P. Yang, Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data, Biometrika 85 (1998), pp. 809–822.
  • Z. Hua, Bayesian Analysis of Varying Coefficient Models and Applications. PhD thesis, University of North Carolina at Chapel Hill, 2011.
  • J.Z. Huang, C.O. Wu, and L. Zhou, Varying-coefficient models and basis function approximations for the analysis of repeated measurements, Biometrika 89 (2002), pp. 111–128.
  • S. Jeong, M. Park, and T. Park, Analysis of binary longitudinal data with time-varying effects, Comput. Stat. Data. Anal. 112 (2017), pp. 145–153.
  • S. Jeong, Park, T., et al., Bayesian semiparametric inference on functional relationships in linear mixed models, Bayesian Anal. 11 (2016), pp. 1137–1163.
  • M.M. Lederman, E. Connick, A. Landay, D.R. Kuritzkes, J. Spritzler, B.L. Kotzin, L. Fox, M.H. Chiozzi, J.M. Leonard, F. Rousseau, M. Wade, J.D. Roe, A. Martinez, and H. Kessler, Immunologic responses associated with 12 weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: results of aids clinical trials group protocol 315, J. Infect. Dis. 178 (1998), pp. 70–79.
  • R. Li and H. Liang, Variable selection in semiparametric regression modeling, Ann. Stat. 36 (2008), pp. 261.
  • H. Liang, H. Wu, and R.J. Carroll, The relationship between virologic and immunologic responses in aids clinical research using mixed-effects varying-coefficient models with measurement error, Biostatistics 4 (2003), pp. 297–312.
  • D.Y. Lin and Z. Ying, Semiparametric and nonparametric regression analysis of longitudinal data, J. Am. Stat. Assoc. 96 (2001), pp. 103–126.
  • X. Lin and R.J. Carroll, Nonparametric function estimation for clustered data when the predictor is measured without/with error, J. Am. Stat. Assoc. 95 (2000), pp. 520–534.
  • T.D. Little, P. Deboeck, and W. Wu, Longitudinal data analysis. Emerging Trends in the Social and Behavioral Sciences: An Interdisciplinary, Searchable, and Linkable Resource, (2015). pp 1–17. Wiley Online Library. https://doi.org/https://doi.org/10.1002/9781118900772.etrds0208
  • X. Liu, Methods and Applications of Longitudinal Data Analysis, Elsevier, 2015.
  • T. Lu and Y. Huang, Bayesian inference on mixed-effects varying-coefficient joint models with skew-t distribution for longitudinal data with multiple features, Stat. Methods. Med. Res. 26 (2017), pp. 1146–1164.
  • Y. Lu and R. Zhang, Smoothing spline estimation of generalised varying-coefficient mixed model, J. Nonparametr. Stat. 21 (2009), pp. 815–825.
  • M. Memmedli and A. Nizamitdinov, An application of various nonparametric techniques by nonparametric regression splines, Int. J. Math. Models Methods Appl. Sci. 6 (2012), pp. 106–113.
  • G. Molenberghs, G. Fitzmaurice, M.G. Kenward, A. Tsiatis, and G. Verbeke, Handbook of Missing Data Methodology, CRC Press, 2014.
  • M. Nobles, N. Serban, and J. Swann, Spatial accessibility of pediatric primary healthcare: measurement and inference, Ann. Appl. Stat. 8 (2014), pp. 1922–1946.
  • J.T. Ormerod and M.P. Wand, Explaining variational approximations, Am. Stat. 64 (2010), pp. 140–153.
  • A. Qu and R. Li, Quadratic inference functions for varying-coefficient models with longitudinal data, Biometrics 62 (2006), pp. 379–391.
  • J.O. Ramsay, G. Hooker, and S. Graves, Functional data analysis with r and matlab, (2009).
  • J.A. Rice and C.O. Wu, Nonparametric mixed effects models for unequally sampled noisy curves, Biometrics 57 (2001), pp. 253–259.
  • D. Ruppert, M.P. Wand, and R.J. Carroll, Semiparametric Regression, Vol. 12, Cambridge university press, 2003.
  • D. Senturk, L.S. Dalrymple, S.M. Mohammed, G.A. Kaysen, and D.V. Nguyen, Modeling time-varying effects with generalized and unsynchronized longitudinal data, Medicine¡/DIFdel¿Stat. Med. 32 (2013), pp. 2971–2987.
  • D. Senturk and H.G. Muller, Generalized varying coefficient models for longitudinal data, Biometrika 95 (2008), pp. 653–666.
  • D. Senturk and H.G. Muller, Functional varying coefficient models for longitudinal data, J. Am. Stat. Assoc. 105 (2010), pp. 1256–1264.
  • N. Serban, A space–time varying coefficient model: the equity of service accessibility, Ann. Appl. Stat. 5 (2011), pp. 2024–2051.
  • J. Sosa and L.G. Diaz, Random time-varying coefficient model estimation through radial basis functions, Rev. Colom. De Estadistica 35 (2012), pp. 167–184.
  • X. Tan, M.P. Shiyko, R. Li, Y. Li, and L. Dierker, A time-varying effect model for intensive longitudinal data, Psychol. Methods. 17 (2012), pp. 61.
  • L.A. Waller, L. Zhu, C.A. Gotway, D.M. Gorman, and P.J. Gruenewald, Quantifying geographic variations in associations between alcohol distribution and violence: a comparison of geographically weighted regression and spatially varying coefficient models, Stoch. Environ. Res. Risk. Assess. 21 (2007), pp. 573–588.
  • H. Wang and Y. Xia, Shrinkage estimation of the varying coefficient model, J. Am. Stat. Assoc. 104 (2009), pp. 747–757.
  • H.J. Wang, Z. Zhu, and J. Zhou, Quantile regression in partially linear varying coefficient models, Ann. Stat. 37 (2009), pp. 3841–3866.
  • L. Wang, H. Li, and J.Z. Huang, Variable selection in nonparametric varying-coefficient models for analysis of repeated measurements, J. Am. Stat. Assoc. 103 (2008), pp. 1556–1569.
  • Y. Wang, Varying-coefficient models: New models, inference procedures, and applications, (2007).
  • L. Wasserman, Nonparametric Statistics, Springer-Verlag, New York, 2006.
  • F. Wei, J. Huang, and H. Li, Variable selection and estimation in high-dimensional varying-coefficient models, Stat. Sin. 21 (2011), pp. 1515.
  • C.O. Wu and C.T. Chiang, Kernel smoothing on varying coefficient models with longitudinal dependent variable, Stat. Sin. 10 (2000), pp. 433–456.
  • C.O. Wu, C.T. Chiang, and D.R. Hoover, Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data, J. Am. Stat. Assoc. 93 (1998), pp. 1388–1402.
  • C.O. Wu and X. Tian, Nonparametric estimation of conditional distributions and rank-tracking probabilities with time-varying transformation models in longitudinal studies, J. Am. Stat. Assoc. 108 (2013), pp. 971–982.
  • C.O. Wu and X. Tian, Nonparametric Models for Longitudinal Data: With Implementation in R, CRC Press, 2018.
  • C.O. Wu, X. Tian, and J. Yu, Nonparametric estimation for time-varying transformation models with longitudinal data, J. Nonparametr. Stat. 22 (2010), pp. 133–147.
  • H. Wu and H. Liang, Backfitting random varying-coefficient models with time-dependent smoothing covariates, Scan. J. Stat. 31 (2004), pp. 3–19.
  • H. Wu and J.T. Zhang, Local polynomial mixed-effects models for longitudinal data, J. Am. Stat. Assoc. 97 (2002), pp. 883–897.
  • H. Wu and J.T. Zhang, Nonparametric Regression Methods for Longitudinal Data Analysis, John Wiley and Sons, 2006.
  • S.L. Zeger and P.J. Diggle, Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters, Biometrics 30 (1994), pp. 689–699.
  • D. Zhang, X. Lin, J. Raz, and M. Sowers, Semiparametric stochastic mixed models for longitudinal data, J. Am. Stat. Assoc. 93 (1998), pp. 710–719.
  • J.T. Zhang, Analysis of Variance for Functional Data, CRC Press, 2013.

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