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Abstract
In this paper, we consider variable selection problem for general transformation models with ranking data by penalized maximum log-marginal likelihood approach. We incorporate smoothly clipped absolute deviation (SCAD), lasso and hard thresholding penalties into penalty term. With some conditions and proper penalties, we show that the corresponding penalized estimates are √n-consistent and enjoy oracle properties. We also propose a three-step Monte Carlo Markov chain stochastic approximation algorithm for our proposed procedures. With the proposed procedure, we not only can select important variables but also are able to estimate corresponding effects. Through some simulation examples and a Hong Kong horse racing data analysis, we illustrate that our proposed procedure uniformly works very well for moderate sample size.
Acknowledgements
We are grateful to the editor, associate editor and referees for their helpful comments that led to the revised version of this paper. This work was partially supported by Humanities and Social Fund of Ministry of Education in China (12YJC910004), PhD Teacher's Research Support Project Foundation of Jiangsu Normal University (11XRL31) and National Natural Science Foundation of China (11171112).