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稀疏高维加性模型中的统计推断AI 解读

In this paper, we discuss the estimation of a nonparametric component f1 of a nonparametric additive model Y=f1(X1)+⋯+fq(Xq)+ϵ. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f1 in the oracle model Z=f1(X1)+ϵ, for which the additive components f2,…,fq are known. We construct a two-step presmoothing-and-resmoothing…

自适应 Lasso 的扰动自助法AI 解读

The Adaptive Lasso (Alasso) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] as a modification of the Lasso for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] established that the Alasso estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain…