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Inference on Parameters of Directional Distributions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kumar, Somesh |
| Copyright Year | 1992 |
| Abstract | R require that the estimation space be chosen such that it is the convex closure of the parameter space. In this presentation, we extend this concept to the problem of estimating circular parameters of directional distributions having support as a circle, torus or cylinder. We observe that transition from Euclidean setting to circular one offers big surprises. As directional distributions are of curved nature, existing methods for distributions with parameters taking values in p R are not immediately applicable here. Circle is the simplest one-dimensional Riemannian manifold. Concepts of convexity, projection, etc. on manifolds are employed to develop sufficient conditions for obtaining improved estimators for circular parameters. Further, invariance under a compact group of transformations is introduced in the estimation problem and a complete class result for equivariant estimators is proved. This extends the results of Moors (Journal of Americal Statistical Association, 1981) and Kumar and Sharma (Statistics and Decisions, 1992) on p R to circles. The findings are of special interest to the case when circular parameter is truncated. The results are applied to a wide range of directional distributions to derive improved estimators of circular parameters. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://louisville.edu/sphis/bb/abstract_somesh_kumar |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
