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Quasi‐Likelihood Regression with Multiple Indices and Smooth Link and Variance Functions

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  • Jeng‐Min Chiou
  • Hans‐Georg Müller

Abstract

. A flexible semi‐parametric regression model is proposed for modelling the relationship between a response and multivariate predictor variables. The proposed multiple‐index model includes smooth unknown link and variance functions that are estimated non‐parametrically. Data‐adaptive methods for automatic smoothing parameter selection and for the choice of the number of indices M are considered. This model adapts to complex data structures and provides efficient adaptive estimation through the variance function component in the sense that the asymptotic distribution is the same as if the non‐parametric components are known. We develop iterative estimation schemes, which include a constrained projection method for the case where the regression parameter vectors are mutually orthogonal. The proposed methods are illustrated with the analysis of data from a growth bioassay and a reproduction experiment with medflies. Asymptotic properties of the estimated model components are also obtained.

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  • Jeng‐Min Chiou & Hans‐Georg Müller, 2004. "Quasi‐Likelihood Regression with Multiple Indices and Smooth Link and Variance Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 367-386, September.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:367-386
    DOI: 10.1111/j.1467-9469.2004.02-117.x
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    Cited by:

    1. Shang, Shulian & Liu, Mengling & Zeleniuch-Jacquotte, Anne & Clendenen, Tess V. & Krogh, Vittorio & Hallmans, Goran & Lu, Wenbin, 2013. "Partially linear single index Cox regression model in nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 199-212.

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