文章基本信息

标题：Adaptive variable selection in nonparametric sparse additive models
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作者：Cristina Butucea ; Natalia Stepanova
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2017
卷号：11
期号：1
页码：2321-2357
DOI：10.1214/17-EJS1275
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon $. We assume that $f$ belongs to a class of smooth functions in $L_{2}([0,1]^{d})$ and has an additive sparse structure determined by the parameter $s$, the number of non-zero univariate components contributing to $f$. We are interested in the case when $d=d_{\varepsilon }\to \infty $ as $\varepsilon \to 0$ and the parameter $s$ stays “small” relative to $d$. With these assumptions, the recovery problem in hand becomes that of determining which sparse additive components are non-zero.