Confidence balls in Gaussian regression

Abstract

Starting from the observation of an R^n-Gaussian vector of mean f and covariance matrix σ^2 I_n (I_n is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.

Cited by in corpus (9)

• Confidence bands in density estimation
• Confidence sets in sparse regression
• On adaptive inference and confidence bands
• Adaptive nonparametric confidence sets
• Adaptive confidence balls
• Conditional predictive inference post model selection
• Inference for the dark energy equation of state using Type IA supernova data
• Testing the regularity of a smooth signal
• Honest confidence sets for high-dimensional regression by projection and shrinkage