作者：Dette, Holger; Melas, Viatcheslav B.
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p - 1 any optimal design can be based on at most p design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499 - 2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon o...
作者：Rigollet, Philippe; Tsybakov, Alexandre
作者单位：Princeton University; Institut Polytechnique de Paris; ENSAE Paris
摘要：In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in this setup is to assume that the linear combination is sparse in some sense, for example, that it involves only few covariates. We consider a general, nonnecessarily linear, regression with Gaussian noise and study a related question, that is, to find a lin...
