| Summary: | 碩士 === 國立政治大學 === 統計研究所 === 102 === Variable selection of a regression model is an essential topic. In 1996, Tibshirani proposed a method called Lasso (Least Absolute Shrinkage and Selection Operator), which completes the matter of selecting variable set while estimating the parameters. However, the original version of Lasso does not provide a way for making inference. Therefore, the significance test for lasso proposed by Lockhart et al. in 2014 is an important breakthrough. Based on the similarity of construction of statistics between Lasso significance test and forward selection method, continuing the comparisons between the two methods from Lockhart et al. (2014), we propose an improved version of forward selection method by bootstrap. And at the second half of our research, we compare the variable selection results of Lasso, Lasso significance test, forward selection, forward selection by AIC, and forward selection by bootstrap. We find that although the Type I error probability for Lasso Significance Test is small, the testing method is too conservative for including new variables. On the other hand, the Type I error probability for forward selection by bootstrap is also small, yet it is more aggressive in including new variables. Therefore, based on our simulation results, the bootstrap improving forward selection is rather an ideal variable selecting method.
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