Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood

References

• Brumback B.A., and Rice J.A. (1998), ‘Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves (with discussion)’, Journal of the American Statistical Association, 93, 961–994. doi: 10.1080/01621459.1998.10473755
   Web of Science ®Google Scholar
• Cai Z., Fan J., and Li R. (2000), ‘Efficient Estimation and Inferences for Varying-coefficient Models’, Journal of the American Statistical Association, 95, 888–902. doi: 10.1080/01621459.2000.10474280
   Web of Science ®Google Scholar
• Cao Y., Lin H., Wu T.Z., and Yu Y. (2010), ‘Penalized Spline Estimation for Functional Coefficient Regression Models’, Computational Statistics and Data Analysis, 54, 891–905. doi: 10.1016/j.csda.2009.09.036
   PubMed Web of Science ®Google Scholar
• Chen R., and Tsay R.S. (1993), ‘Functional-coefficient Autoregressive Models’, Journal of the American Statistical Association, 88, 298–308.
   Web of Science ®Google Scholar
• Cleveland W., Grosse E., and Shyu W. (1991), ‘Local Regression Models’, in Statistical Models in S (2nd ed.), eds. J. Chambers and T. Hastie, Pacific Grove, CA: Wadsworth and Brooks/Cole, pp. 309–376.
   Google Scholar
• Eilers P.H.C., and Marx B.D. (1996), ‘Flexible Smoothing with B-splines and Penalities’, Statistical Science, 11, 89–102. doi: 10.1214/ss/1038425655
   Web of Science ®Google Scholar
• Fan J. (1993), ‘Local Linear Regression Smoothers and their Minimax Efficiencies’, The Annals of Statistics, 21, 196–216. doi: 10.1214/aos/1176349022
   Web of Science ®Google Scholar
• Fan J., Farmen M., and Gijbels I. (1998), ‘Local Maximum Likelihood Estimation and Inference’, Journal of the Royal Statistical Society Series B, 60, 591–608. doi: 10.1111/1467-9868.00142
   Google Scholar
• Fan J., and Gijbels I. (1996), Local Polynomial Modelling and its Applications, London: Chapman and Hall.
   Google Scholar
• Fan J., Maity A., Wang Y., and Wu Y. (2013), ‘Parametrically Guided Generalised Additive Models with Application to Mergers and Acquisitions Data’, Journal of Nonparametric Statistics, 25, 109–128. doi: 10.1080/10485252.2012.735233
   PubMed Web of Science ®Google Scholar
• Fan J., Wu Y., and Feng Y. (2009), ‘Local Quasi-likelihood with a Parametric Guide’, The Annals of Statistics, 37, 4153–4183. doi: 10.1214/09-AOS713
   PubMed Web of Science ®Google Scholar
• Fan J., and Zhang W. (1999), ‘Statistical Estimation in Varying Coefficient Models’, The Annals of Statistics, 27, 1491–1518. doi: 10.1214/aos/1017939139
   Web of Science ®Google Scholar
• Fan J., and Zhang W. (2008), ‘Statistical Methods with Varying Coefficient Models’, Statistics and Its Interface, 1, 179–195. doi: 10.4310/SII.2008.v1.n1.a15
   PubMed Web of Science ®Google Scholar
• Glad I.K. (1998), ‘Parametrically Guided Non-parametric Regression’, Scandinavian Journal of Statistics, 25, 649–668. doi: 10.1111/1467-9469.00127
   Web of Science ®Google Scholar
• Hastie T., and Tibshirani R. (1993), ‘Varying-coefficient Models’, Journal of the Royal Statistical Society Series B, 55, 757–796.
   Google Scholar
• Hjort N.L., and Glad I.K. (1995), ‘Nonparametric Density Estimation with a Parametric Start’, The Annals of Statistics, 23, 882–904. doi: 10.1214/aos/1176324627
   Web of Science ®Google Scholar
• Holdeman J.T. (1969), ‘A Method for the Approximation of Functions Defined by Formal Series Expansions in Orthogonal Polynomials’, Mathematics of Computation, 23, 275–287. doi: 10.1090/S0025-5718-1969-0251412-1
   Web of Science ®Google Scholar
• Hoover D.R., Rice J.A., Wu C.O., and Yang L.P. (1998), ‘Nonparametric Smoothing Estimates of Time-varying Coefficient Models with Longitudinal Data’, Biometrika, 85, 809–822. doi: 10.1093/biomet/85.4.809
   Web of Science ®Google Scholar
• Huang J.Z., and Shen H. (2004), ‘Functional Coefficient Regression Models for Nonlinear Time Series: A Polynomial Spline Approach’, Scandinavian Journal of Statistics, 31, 515–534. doi: 10.1111/j.1467-9469.2004.00404.x
   Web of Science ®Google Scholar
• Lederman M.M., Connick E., Landay A., Kuritzkes D.R., Spritzler J., St. Clair M., Kotzin B.L., Fox L., Chiozzi M.H., and Leonard J.M. et al. (2002), ‘Immunologic Responses Associated with 12 Weeks of Combination Antiretroviral Therapy Consisting of Zidovudine, Lamivudine, and Ritonavir: Results of AIDS Clinical Trials Group Protocol 315’, The Journal of Infectious Diseases, 179, 70–79.
   Google Scholar
• Liang H., Wu H., and Carroll R.J. (2003), ‘The Relationship between Virologic and Immunologic Responses in AIDS Clinical Research using Mixed-effects Varying-coefficient Models with Measurement Error’, Biostatistics, 4, 297–312. doi: 10.1093/biostatistics/4.2.297
   PubMed Web of Science ®Google Scholar
• Ma S., Yang L., Romero R., and Cui Y. (2011), ‘Varying Coefficient Model for Gene-environment Interaction: A Non-linear Look’, Bioinformatics, 27, 2119–2126. doi: 10.1093/bioinformatics/btr318
   PubMed Web of Science ®Google Scholar
• Martins-Filho C., Mishra S., and Ullah A. (2008), ‘A Class of Improved Parametrically Guided Nonparametric Regression Estimators’, Econometric Reviews, 27, 542–573. doi: 10.1080/07474930801960444
   Web of Science ®Google Scholar
• Nelder J.A., and Wedderburn R.W.M. (1972), ‘Generalized Linear Models’, Journal of the Royal Statistical Society Series A, 135, 370–384. doi: 10.2307/2344614
   Web of Science ®Google Scholar
• Wedderburn R.W.M. (1974), ‘Quasi-likelihood Functions, Generalized Linear Models, and the Gauss-Newton Method’, Biometrika, 61, 439–447.
   Web of Science ®Google Scholar
• White H. (1982), ‘Maximum Likelihood Estimation of Misspecified Models’, Econometrica, 50, 1–25. doi: 10.2307/1912526
   Web of Science ®Google Scholar
• Wood S.N. (2006), Generalized Additive Models: An Introduction with R, Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Wu H., and Wu L. (2002), ‘Identification of Significant Host Factors for HIV Dynamics Modelled by Non-linear Mixed-effects Models’, Statistics in Medicine, 21, 753–771. doi: 10.1002/sim.1015
   PubMed Web of Science ®Google Scholar