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Minimax Risk: Pinsker Bound
COMMUNICATION THEORY, STATISTICAL DENSITY ESTIMATION FISHER INFORMATION KERNEL ESTIMATORS LINEAR ESTIMATORS, BAYES LOCAL ASYMPTOTIC NORMALITY METHOD OF SIEVES MINIMAX ESTIMATION NOISE (SIGNAL PROCESSING IN THE PRESENCE OF ) PREDICTION AND FILTERING LINEAR SIEVES, METHOD OF SPECTRAL ANALYSIS SHRINKAGE ESTIMATORS SMOOTHNESS PRIORS SOBOLEV SPACES SPLINE FUNCTIONS STATIONARY PROCESSES STEIN EFFECT
2015/8/25
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...
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...
On minimax estimation of a sparse normal mean vector
nearly black object robustness white noise model
2015/8/20
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...
Minimax Bayes, asymptotic minimax and sparse wavelet priors
Minimax Decision theory Minimax Bayes estimation
2015/8/20
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 ...