##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## William E. Strawderman

#### Rutgers University

## Improved estimation of restricted parameters

##### Abstract:

We consider the problem of estimating a vector of location parameters restricted to a cone in the presence of an unknown scale parameter. Examples include estimating the location vector when the parameter ordering is known (or partially known), or when it is known that all means are positive. A standard estimator when sampling from a multivariate normal distribution is the MLE. In the unrestricted case, this estimator is the vector of sample means, which is dominated (in three and higher dimensions) by the James-Stein estimator among others. We study improvements of the James-Stein type for the restricted parameter case in the general setting of a spherical symmetry location family. The development is based on a general result that shows how improved estimators of location in the multivariate normal case with known scale can be extended to give improved estimators in the general spherically symmetric case with unknown scale.

Host: Dimitris Politis

### April 14, 2005

### 4:00 PM

### AP&M 6438

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