The admissibility of the empirical distribution function (Q1063964)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The admissibility of the empirical distribution function |
scientific article; zbMATH DE number 3919532
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The admissibility of the empirical distribution function |
scientific article; zbMATH DE number 3919532 |
Statements
The admissibility of the empirical distribution function (English)
0 references
1985
0 references
Consider the problem of estimating an unknown distribution function F from the class of all distribution functions given a random sample of size n from F. It is proved that the empirical distribution function is admissible for the loss functions \[ L(F,\hat F)=\int (\hat F(t)-F(t))^ 2(F(t))^ a(1-F(t))^ bdW(t) \] for any \(a<1\) and \(b<1\) and finite measure W. Related results for simultaneous estimation of distribution functions and for finite population sampling are also given.
0 references
weighted quadratic loss
0 references
simple random sampling without replacement
0 references
multinomial distribution
0 references
multivariate hypergeometric distribution
0 references
empirical distribution
0 references
simultaneous estimation
0 references
finite population sampling
0 references
