The Asymptotic Inadmissibility of the Sample Distribution Function
Read, R. R.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 89-95 / Harvested from Project Euclid
Given a sample of size $n$, a continuous estimator for a distribution $F$ (based on Pyke's modified sample distribution) is shown to have the property that its expected squared error, for almost all $x$ in the positive sample space of $F$, is no larger than that of the sample distribution function given $F$ and $n$ sufficiently large. Letting risk be given by the expected squared error integrated with respect to $F$, it is shown that this estimator dominates both the sample distribution and the other best invariant estimator found by Aggarwal, given $F$ and $n$ sufficiently large. Other common estimators cannot serve in this dominating role. Explicit calculation of risk is made when $F$ is the uniform distribution. In this case the estimator strictly dominates the sample distribution for all $n \geqq 1$.
Publié le : 1972-02-14
Classification: 
@article{1177692704,
     author = {Read, R. R.},
     title = {The Asymptotic Inadmissibility of the Sample Distribution Function},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 89-95},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692704}
}
Read, R. R. The Asymptotic Inadmissibility of the Sample Distribution Function. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  89-95. http://gdmltest.u-ga.fr/item/1177692704/