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

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  • Clemontina A. Davenport
  • Arnab Maity
  • Yichao Wu

Abstract

Varying coefficient models (VCMs) allow us to generalise standard linear regression models to incorporate complex covariate effects by modelling the regression coefficients as functions of another covariate. For nonparametric varying coefficients, we can borrow the idea of parametrically guided estimation to improve asymptotic bias. In this paper, we develop a guided estimation procedure for the nonparametric VCMs. Asymptotic properties are established for the guided estimators and a method of bandwidth selection via bias-variance tradeoff is proposed. We compare the performance of the guided estimator with that of the unguided estimator via both simulation and real data examples.

Suggested Citation

  • Clemontina A. Davenport & Arnab Maity & Yichao Wu, 2015. "Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 195-213, June.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:195-213
    DOI: 10.1080/10485252.2015.1026903
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    References listed on IDEAS

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    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. Cao, Yanrong & Lin, Haiqun & Wu, Tracy Z. & Yu, Yan, 2010. "Penalized spline estimation for functional coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 891-905, April.
    3. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    4. Jianqing Fan & Arnab Maity & Yihui Wang & Yichao Wu, 2013. "Parametrically guided generalised additive models with application to mergers and acquisitions data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 109-128, March.
    5. Carlos Martins-Filho & Santosh Mishra & Aman Ullah, 2008. "A Class of Improved Parametrically Guided Nonparametric Regression Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 542-573.
    6. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
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    Cited by:

    1. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Parametrically guided local quasi-likelihood with censored data," LIDAM Discussion Papers ISBA 2016011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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