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Globally consistent model selection in semi-parametric additive coefficient models

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  • Shuping Jiang
  • Lan Xue

Abstract

We study a penalised polynomial spline (PPS) method for model selection in additive coefficient models. It approximates nonparametric coefficient functions by polynomial splines and minimises the sum of squared errors subject to an additive penalty on the norms of spline functions. For non-convex penalty functions such as smoothly clipped absolute deviation (SCAD) penalty, we investigate the asymptotic properties of the global solution of the non-convex objective function. We establish explicitly that the oracle estimator is the global solution with probability approaching one. Therefore, the global solution enjoys both model estimation and selection consistency. In the literature, the asymptotic properties of local solutions rather than global solutions are well-established for non-convex penalty functions. Our theoretical results broaden the traditional understanding of the PPS method. Extensive Monte Carlo simulation studies show the proposed method performs well numerically. We also illustrate the use of the proposed method by analysing a housing price data set.

Suggested Citation

  • Shuping Jiang & Lan Xue, 2015. "Globally consistent model selection in semi-parametric additive coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 532-551, December.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:532-551
    DOI: 10.1080/10485252.2015.1083566
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    References listed on IDEAS

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    1. Xue, Lan & Qu, Annie & Zhou, Jianhui, 2010. "Consistent Model Selection for Marginal Generalized Additive Model for Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1518-1530.
    2. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    3. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    4. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    7. Timothy J. Fik & David C. Ling & Gordon F. Mulligan, 2003. "Modeling Spatial Variation in Housing Prices: A Variable Interaction Approach," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(4), pages 623-646, December.
    8. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    9. Shuping Jiang & Lan Xue, 2013. "Lag selection in stochastic additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 129-146, March.
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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