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Variable selection for general transformation models with ranking data

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.