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Proper Bayesian estimating equation based on Hilbert space method

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  • Lin, Lu
  • Tan, Lin

Abstract

This paper uses Hilbert space method to introduce and investigate the validity of Bayesian estimating equation. A validity for Hilbert-based Bayesian estimating function is established via the Hilbert-based unbiasedness and information unbiasedness. As an application, the newly proposed method is adopted to construct an estimating equation for nonlinear regression model. Furthermore, the new notion is employed to lay a theoretical foundation for the penalty-based methods such as penalized likelihood and penalized least squares.

Suggested Citation

  • Lin, Lu & Tan, Lin, 2008. "Proper Bayesian estimating equation based on Hilbert space method," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1119-1127, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1119-1127
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    References listed on IDEAS

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    1. 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.
    2. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    3. Lu Lin, 2004. "Generalized quasi-likelihood," Statistical Papers, Springer, vol. 45(4), pages 529-544, October.
    4. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
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