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Partially linear single-index beta regression model and score test

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  • Zhao, Weihua
  • Zhang, Riquan
  • Huang, Zhensheng
  • Feng, Jingyan
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    Abstract

    An important model in handling the multivariate data is the partially linear single-index regression model with a very flexible distribution--beta distribution, which is commonly used to model data restricted to some open intervals on the line. In this paper, the score test is extended to the partially linear single-index beta regression model. The penalized likelihood estimation based on P-spline is proposed. Based on the estimation, the score test statistics about varying dispersion parameter is given. Its asymptotical property is investigated. Both simulated examples are used to illustrate our proposed methods.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 103 (2012)
    Issue (Month): 1 (January)
    Pages: 116-123

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    Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:116-123

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    Related research

    Keywords: Partially linear single-index model Beta regression P-spline Penalized likelihood estimation Score test;

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    1. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(2), pages 277-294, June.
    2. Espinheira, PatriĀ­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    3. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single-index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570.
    4. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    5. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
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