Bootstrap Calibration, Model Selection and Tree-Structured Methods

摘要

Several problems in variable selection and decision trees were solved. In thecase of linear regression models with increasing number of covariates, a method based on ordering the covariates in terms of their t-statistics is shown to be asymptotically consistent as the sample size increases. This result holds for the fixed design situation as well as that of random covariates. A new unbiased method of split selection for classification trees was developed and implemented into computer software. The method is unbiased in the sense that when all the covariates are unrelated to the response variable, each covariate has an equal chance of being selected to split a node. No previous algorithm has this property. Bootstrap calibration plays a critical role in the algorithm. Empirical evaluations of the algorithm show that it is as accurate as the best classifiers from the statistical and computer science literature. It has the additional benefit of being one of the fastest algorithms.