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Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal grad...
We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and...
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...
Consider estimating the mean vector  from data Nn(; 2I ) with lq norm loss, q  1, when  is known to lie in an n-dimensional lp ball, p 2 (0; 1). For large n, the ratio of minimax linear risk to...
Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contaminatio...
Pinsker(1980) gave a precise asymptotic evaluation of the minimax mean squared error of estimation of a signal in Gaussian noise when the signal is known a priori to lie in a compact ellipsoid in Hi...
We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple ...
We study the problem of estimating  from data Y  N(; 2 ) under squared-error loss. We de ne three new scalar minimax problems in which the risk is weighted by the size of . Simple thresholding...
We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections o...
Abstract: In this paper, a lower bound is determined in the minimax sense for change point estimators of the first derivative of a regression function in the fractional white noise model. Similar mini...
We address the problem of density estimation with L p–loss by selection of kernel estimators. We develop a selection procedure and derive corresponiding L p–risk oracle inequalities. It is shown that ...
Let X1, X2 be independent random variables from gamma populations Π1,Π2 with common arbitrary known shape parameter α and unknown scale parameters θ1, θ2 respectively. Suppose X(1), X(2) be the order ...
In this paper, a Newton like method for solving minimax optimization problems was proposed. The method belong to sequential quadratic programming method, the Hessian of quadratic programming subproble...
该文在一般正态随机效应线性模型中研究了随机回归系数和参数的估计问题. 在二次损失下,得到了线性可估函数在一切估计类中的唯一Minimax估计.
The paper deals with a smoothing procedure for parametric minimax-functions, arising from parameter dependend convex-concave games. In this framework generalized max-functions (i.e. maximum value func...

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