The Annals of Statistics

On nonparametric confidence intervals

Mark G. Low

Full-text: Open access

Abstract

An inequality is given for the expected length of a confidence interval given that a particular distribution generated the data and assuming that the confidence interval has a given coverage probability over a family of distributions. As a corollary, attempts to adapt to the regularity of the true density within derivative smoothness classes cannot improve the rate of convergence of the length of the confidence interval over minimax fixed-length intervals and still maintain uniform coverage probability. However, adaptive confidence intervals can attain improved rates of convergence in some other classes of densities, such as those satisfying a shape restriction.

Article information

Source
Ann. Statist., Volume 25, Number 6 (1997), 2547-2554.

Dates
First available in Project Euclid: 30 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1030741084

Digital Object Identifier
doi:10.1214/aos/1030741084

Mathematical Reviews number (MathSciNet)
MR1604412

Zentralblatt MATH identifier
0894.62055

Subjects
Primary: 62G07: Density estimation

Keywords
Confidence intervals density estimation

Citation

Low, Mark G. On nonparametric confidence intervals. Ann. Statist. 25 (1997), no. 6, 2547--2554. doi:10.1214/aos/1030741084. https://projecteuclid.org/euclid.aos/1030741084


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