[in Journal: Series in Biostatistics] AND [Keyword: Projection] : Search

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[in Journal: Series in Biostatistics] AND [Keyword: Projection] (1)	30 Mar 2025	Run
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[in Journal: Stochastics and Dynamics] AND [Keyword: Randomness] (1)	30 Mar 2025	Run

chapterNo Access
ESTIMATION OF SYMMETRIC DISTRIBUTIONS SUBJECT TO A PEAKEDNESS ORDER
- Javier Rojo and
- José Batún-Cutz
Advances in Statistical Modeling and Inference01 Mar 2007
Preview Abstract
A distribution function F is more peaked about a point a than the distribution G is about the point b if F((x + a)⁻) − F(−x + a) ≥ G((x + b)⁻) − G(−x + b) for every x > 0. The problem of estimating symmetric distribution functions F or G, or both, under this constraint is considered in this paper. It turns out that the proposed estimators are projections of the empirical distribution function onto suitable convex sets of distribution functions. As a consequence, the estimators are shown to be strongly uniformly consistent. The asymptotic distribution theory of the estimators is also discussed.

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