**ERIC Number:**ED079400

**Record Type:**RIE

**Publication Date:**1973-Jun

**Pages:**28

**Abstractor:**N/A

**Reference Count:**0

**ISBN:**N/A

**ISSN:**N/A

Combining Unbiased Estimates of a Parameter Known to be Positive.

Stroud, T. W. F.

The statistician has n independent estimates of a parameter he knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the n estimates are to be combined into a single number, we compare the obvious rule, that of averaging the n values and taking the positive part of the result, with that of averaging the positive parts. Although the estimator generated by the second rule is not consistent, it is shown by numerical calculation that for small n it has a smaller mean square error than the first over a considerable region of the parameter space, and that for n = 2 or 3 the second is minimax relative to the first over a region consisting of almost the whole parameter space. The distribution of each of the n estimates is assumed to be either Gaussian or the distribution of a weighted difference of two independent chi-squares with known degrees of freedom, as in one-way components of variance. Some other simply calculated estimators, including the positive part of the median, are studied for the chi-square difference case with (2,2) degrees of freedom and n = 3. (Author)

**Publication Type:**N/A

**Education Level:**N/A

**Audience:**N/A

**Language:**N/A

**Sponsor:**N/A

**Authoring Institution:**Educational Testing Service, Princeton, NJ.