Open Access
November 2016 Methods for improving estimators of truncated circular parameters
Kanika, Somesh Kumar
Bernoulli 22(4): 2521-2547 (November 2016). DOI: 10.3150/15-BEJ736


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.


Download Citation

Kanika. Somesh Kumar. "Methods for improving estimators of truncated circular parameters." Bernoulli 22 (4) 2521 - 2547, November 2016.


Received: 1 January 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 06603452
MathSciNet: MR3498036
Digital Object Identifier: 10.3150/15-BEJ736

Keywords: Admissibility , convexity , directional data , Invariance , projection , truncated estimation problem

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
Back to Top