Universal Adaptive Estimations and Confidence Intervals in the Nonparametric Statistics

Eugene Ostrovsky; Leonid Sirota

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arXiv · math/0406535

Universal Adaptive Estimations and Confidence Intervals in the Nonparametric Statistics

Eugene Ostrovsky·Leonid Sirota

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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 $L_2$, and confidence intervals, also adaptive, are constructed on their basis for the estimated functions in an integral norm.

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Eugene Ostrovsky, Leonid Sirota. 2004-06-25. Universal Adaptive Estimations and Confidence Intervals in the Nonparametric Statistics. https://arxiv.org/abs/math/0406535

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