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Functional quasi‐likelihood regression models with smooth random effects

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  • Jeng‐Min Chiou
  • Hans‐Georg Müller
  • Jane‐Ling Wang

Abstract

Summary. We propose a class of semiparametric functional regression models to describe the influence of vector‐valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single‐index models that include unknown smooth link and variance functions. The parametric components of the single‐index models are estimated via quasi‐score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit‐flies (medflies).

Suggested Citation

  • Jeng‐Min Chiou & Hans‐Georg Müller & Jane‐Ling Wang, 2003. "Functional quasi‐likelihood regression models with smooth random effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 405-423, May.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:405-423
    DOI: 10.1111/1467-9868.00393
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    Citations

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    Cited by:

    1. Philip T. Reiss & Lei Huang & Pei‐Shien Wu & Huaihou Chen & Stan Colcombe, 2017. "Pointwise influence matrices for functional‐response regression," Biometrics, The International Biometric Society, vol. 73(4), pages 1092-1101, December.
    2. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2012. "Functional linear regression after spline transformation," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 587-601.
    3. John A. D. Aston & Jeng‐Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317, March.
    4. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.
    5. Jianing Fan & Hans‐Georg Müller, 2022. "Conditional distribution regression for functional responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 502-524, June.
    6. Chen, Xuerong & Li, Haoqi & Liang, Hua & Lin, Huazhen, 2019. "Functional response regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 218-233.
    7. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    8. Li, Pai-Ling & Chiou, Jeng-Min & Shyr, Yu, 2017. "Functional data classification using covariate-adjusted subspace projection," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 21-34.
    9. Mestekemper, Thomas & Kauermann, Göran & Smith, Michael S., 2013. "A comparison of periodic autoregressive and dynamic factor models in intraday energy demand forecasting," International Journal of Forecasting, Elsevier, vol. 29(1), pages 1-12.
    10. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    11. Cardot, Herve & Crambes, Christophe & Kneip, Alois & Sarda, Pascal, 2007. "Smoothing splines estimators in functional linear regression with errors-in-variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4832-4848, June.
    12. Qing-Yan Peng & Jian-Jun Zhou & Nian-Sheng Tang, 2016. "Varying coefficient partially functional linear regression models," Statistical Papers, Springer, vol. 57(3), pages 827-841, September.
    13. Christian Ritz & Jens C. Streibig, 2009. "Functional Regression Analysis of Fluorescence Curves," Biometrics, The International Biometric Society, vol. 65(2), pages 609-617, June.
    14. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2013. "Functional contour regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 1-13.

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