Abstract:
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In this paper, we consider the variable selection problem in semiparametric additive partially linear models for identifying relevant main effects and interactions, while simultaneously naturally enforce the strong hierarchical restriction, that is, an interaction can be included in the model only if both associated main effects are also included in the model. Based on B-splines basis approximation for the nonparametric components, we propose an iterative estimation procedure to fit the model by penalized likelihood with a partial group MCP and use BIC to select the tuning parameters. To further improve the estimation efficiency, we specify the working covariance matrix by maximum likelihood estimation. A set of simulation studies indicate that the proposed method tends to consistently select the true model and works efficiently in estimation and prediction with finite samples, especially when the true model obeys strong hierarchy. Finally, the China Stock Market data are fitted with a semiparametric additive partially linear model to illustrate the proposed method.
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