skip to main content skip to footer

Combining Unbiased Estimates of a Parameter Known to be Positive

Stroud, Thomas W. F.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Mathematical Models, Statistical Analysis


The statistician has n independent estimates of a parameter she knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the 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 estimater 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 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 studies for the chi-square difference case with (2,2) degrees of freedom and n = 3. (Author). (28pp.)

Read More