The penalized profile sampler |
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Authors: | Guang Cheng Michael R. Kosorok |
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Affiliation: | a Department of Statistical Science, Duke University, 214 Old Chemistry Building, Durham, NC 27708, USA b Department of Biostatistics, School of Public Health, University of North Carolina at Chapel Hill, 3101 McGavran-Greenberg Hall, Chapel Hill, NC 27599, USA |
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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. |
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Keywords: | Primary 62G20 62F1 62F15 |
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