Bernoulli

• Bernoulli
• Volume 22, Number 4 (2016), 2521-2547.

Methods for improving estimators of truncated circular parameters

Abstract

In decision theoretic estimation of parameters in Euclidean space $\mathbb{R}^{p}$, the action space is chosen to be the convex closure of the estimand space. In this paper, the concept has been extended to the estimation of circular parameters of distributions having support as a circle, torus or cylinder. As directional distributions are of curved nature, existing methods for distributions with parameters taking values in $\mathbb{R}^{p}$ are not immediately applicable here. A circle is the simplest one-dimensional Riemannian manifold. We employ concepts of convexity, projection, etc., on manifolds to develop sufficient conditions for inadmissibility of estimators for circular parameters. Further invariance under a compact group of transformations is introduced in the estimation problem and a complete class theorem for equivariant estimators is derived. This extends the results of Moors [J. Amer. Statist. Assoc. 76 (1981) 910–915] on $\mathbb{R}^{p}$ to circles. The findings are of special interest to the case when a circular parameter is truncated. The results are implemented to a wide range of directional distributions to obtain improved estimators of circular parameters.

Article information

Source
Bernoulli, Volume 22, Number 4 (2016), 2521-2547.

Dates
First available in Project Euclid: 3 May 2016

https://projecteuclid.org/euclid.bj/1462297688

Digital Object Identifier
doi:10.3150/15-BEJ736

Mathematical Reviews number (MathSciNet)
MR3498036

Zentralblatt MATH identifier
06603452

Citation

Kanika; Kumar, Somesh. Methods for improving estimators of truncated circular parameters. Bernoulli 22 (2016), no. 4, 2521--2547. doi:10.3150/15-BEJ736. https://projecteuclid.org/euclid.bj/1462297688

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