Estimating a Bounded Normal Mean
Reads0
Chats0
TLDR
In this article, it was shown that if the interval is small (approximately two standard deviations wide) then the Bayes rule against a two point prior is the unique minimax estimator under squared error loss.Abstract:
The problem of estimating a normal mean has received much attention in recent years. If one assumes, however, that the true mean lies in a bounded interval, the problem changes drastically. In this paper we show that if the interval is small (approximately two standard deviations wide) then the Bayes rule against a two point prior is the unique minimax estimator under squared error loss. For somewhat wider intervals we also derive sufficient conditions for minimaxity of the Bayes rule against a three point prior.read more
Citations
More filters
Journal ArticleDOI
Geometrizing Rates of Convergence, III
David L. Donoho,Richard C. Liu +1 more
TL;DR: In this paper, it was shown that for well-behaved loss functions, the complexity of the full infinite-dimensional composite testing problem is comparable to the difficulty of the hardest simple two-point testing subproblem.
Journal ArticleDOI
Statistical Estimation and Optimal Recovery
TL;DR: The method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery.
Journal ArticleDOI
Minimax Risk Over Hyperrectangles, and Implications
TL;DR: In this paper, it was shown that the difficulty of estimating the mean of a standard Gaussian shift when that mean lies in an orthosymmetric quadratically convex set in 2-dimensional space is measured by the complexity of the problem.
Journal ArticleDOI
Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising
TL;DR: In this article, the authors present a formula that characterizes the allowed undersampling of generalized sparse objects for approximate message passing (AMP) algorithms for compressed sensing, which are here generalized to employ denoising operators besides the traditional scalar soft thresholding denoiser.
Journal ArticleDOI
Minimax risk over l p -balls for l p -error
TL;DR: In this article, it was shown that the ratio of minimax linear risk to minimax risk can be asymptotically minimax at small signal-to-noise ratios, and within a bounded factor of asymPTotic minimaxity in general.
References
More filters
Journal ArticleDOI
Uniform approximation of minimax point estimates
TL;DR: In this paper, it was shown that an approximation to the minimax estimate uO(x) in the space 5(.. of functions with bounded risk, may be obtained by the minimum estimate UN(X), in the finite dimensional linear space spanned by n basis vectors vi1, * VN of 5(P).