Global risk bounds and adaptation in univariate convex regression
نویسندگان
چکیده
منابع مشابه
Global risk bounds and adaptation in univariate convex regression
We consider the problem of nonparametric estimation of a convex regression function φ0. We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show that the risk is always bounded from above by n−4/5 (up to logarithmic factors) while being much smaller when φ0 is well-approximable by a piecewise affine convex function with not too many affine pieces (in ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2014
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-014-0595-3