Minimum Distance Estimators for Location and Goodness of Fit
- 1 September 1981
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 76 (375) , 663
- https://doi.org/10.2307/2287527
Abstract
A weighted Cramér-von Mises distance between the empirical distribution function and the assumed model F0(x - θ) is minimized to produce estimators θn that are asymptotically normal. If the weight function is taken proportional to (- ln f 0)″/f 0, then θn is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom. Special attention is focused on the limiting distribution of this latter goodness-of-fit statistic in both null and alternative situations.Keywords
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