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The penalized profile sampler

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  • Cheng, Guang
  • Kosorok, Michael R.

Abstract

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method [B.L. Lee, M.R. Kosorok, J.P. Fine, The profile sampler, Journal of the American Statistical Association 100 (2005) 960-969] obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior distribution obtained by multiplying a profiled penalized log-likelihood by a prior for the parametric component, where the profiling and penalization are applied to the nuisance parameter. Because the prior is not applied to the full likelihood, the method is not strictly Bayesian. A benefit of this approximately Bayesian method is that it circumvents the need to put a prior on the possibly infinite-dimensional nuisance components of the model. We investigate the first and second order frequentist performance of the penalized profile sampler, and demonstrate that the accuracy of the procedure can be adjusted by the size of the assigned smoothing parameter. The theoretical validity of the procedure is illustrated for two examples: a partly linear model with normal error for current status data and a semiparametric logistic regression model. Simulation studies are used to verify the theoretical results.

Suggested Citation

  • Cheng, Guang & Kosorok, Michael R., 2009. "The penalized profile sampler," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 345-362, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:345-362
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    References listed on IDEAS

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    1. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    2. Murphy, S. A. & van der Vaart, A. W., 2001. "Semiparametric Mixtures in Case-Control Studies," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 1-32, October.
    3. Shuangge Ma & Michael Kosorok, 2006. "Adaptive penalized M-estimation with current status data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 511-526, September.
    4. Shen X., 2002. "Asymptotic Normality of Semiparametric and Nonparametric Posterior Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 222-235, March.
    5. Lee, Bee Leng & Kosorok, Michael R. & Fine, Jason P., 2005. "The Profile Sampler," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 960-969, September.
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    1. Guang Cheng, 2013. "How Many Iterations are Sufficient for Efficient Semiparametric Estimation?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 592-618, September.

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