偏誤模型下L2Boosting估計法的極限預測方差

Abstract

We examine the stochastic properties of L2Boosting estimator with rigorous treatment. Our research focuses on the weak orthogonal greedy algorithm because of its accessibility to analysis. Under mild conditions, the uniform law of large number of the optimal L2Boosting estimator is established and the uniqueness of the optimal selection path is suggested. Based on the established results, we derive the exact asymptotic form for mean squared prediction error of L2Boosting estimator, and an algebraic tradeoff between squared bias and variance is found. The asymptotic expression serves as preliminaries for the future investigation on the optimal stopping rule of L2Boosting algorithm.