ASYMPTOTICALLY EFFICIENT ESTIMATION BY LOCAL LOCATION-PARAMETER APPROXIMATIONS.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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It is well known that there exist asymptotically efficient estimators for regular location parameter families. Linear combinations of order statistics may be used. Fraser observed that if Fx, theta is any regular stochastically increasing family of distributions and theta sub 1 any fixed parameter value, a transformation S.theta sub 1 exists such that the transformed random variable has approximately a location parameter distribution for theta near theta sub 1. One can therefore estimate theta by using an inefficient but consistent estimator theta prime sub n, applying the transformation S.theta prime sub n to the observations and using the AE sup n estimator for the approximating location parameter family. It is shown that this procedure is asymptotically efficient and an example of its use is given. Author
- Statistics and Probability