The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 6 (1997), 2547-2554.
On nonparametric confidence intervals
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.
Ann. Statist., Volume 25, Number 6 (1997), 2547-2554.
First available in Project Euclid: 30 August 2002
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G07: Density estimation
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