Universal Adaptive Estimations and Confidence Intervals in the Nonparametric Statistics

2004/06/25 by E. Ostrovsky, Eugene Ostrovsky, Ostrovsky, Eugene +3
Computer Science · Environmental Science · Mathematics · #Analysis of environmental and stochastic processes #Image and Signal Denoising Methods #Statistical and numerical algorithms #math.FA #math.PR #msc:14J32

paper · pdf · doi:10.48550/arxiv.math/0406535

arxiv created 2004/06/25 · arxiv updated 2009/12/01

Abstract

The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace compactly embedded in space L₂, and confidence intervals, also adaptive, are constructed on their basis for the estimated functions in an integral norm.

Related

• Adaptive Optimal Nonparametric Regression and Density Estimation Based on Fourier-Legendre Expansion
• Adaptive smoothness of function estimation in the three classical problems of the non-parametrical statistic in the three classical problems of the non-parametrical statistic
• Adaptive Confidence Sets for the Optimal Approximating Model
• Adaptive confidence bands in the nonparametric fixed design regression\n model
• Adaptive estimation of \mathbbL₂-norm of a probability density and related topics I. Lower bounds