A Modi ed Principal Component Technique Based on the LASSO
نویسندگان
چکیده
In many multivariate statistical techniques, a set of linear functions of the original p variables is produced. One of the more dif cult aspects of these techniques is the interpretation of the linear functions, as these functions usually have nonzero coef cients on all p variables. A common approach is to effectively ignore (treat as zero) any coef cients less than some threshold value, so that the function becomes simple and the interpretation becomes easier for the users. Such a procedure can be misleading.There are alternatives to principal componentanalysiswhich restrict the coef cients to a smaller number of possible values in the derivationof the linear functions,or replace the principalcomponentsby “principal variables.” This article introduces a new technique, borrowing an idea proposed by Tibshirani in the context of multiple regressionwhere similar problems arise in interpreting regression equations. This approach is the so-called LASSO, the “least absolute shrinkage and selection operator,” in which a bound is introduced on the sum of the absolute values of the coef cients, and in which some coef cients consequentlybecome zero. We explore some of the propertiesof the new technique,both theoreticallyand using simulationstudies, and apply it to an example.
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