| Title:
|
On the Rao-Blackwell Theorem for fuzzy random variables (English) |
| Author:
|
Lubiano, María Asunción |
| Author:
|
Gil, María Angeles |
| Author:
|
López-Díaz, Miguel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
[167]-175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a previous paper, conditions have been given to compute iterated expectations of fuzzy random variables, irrespectively of the order of integration. In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expected value have been introduced and analyzed. In the present paper we combine the conditions and generalized measure above to state an extension of the basic Rao–Blackwell Theorem. An application of this extension is carried out to construct a proper unbiased estimator of the expected value of a fuzzy random variable in the random sampling with replacement from a finite population. (English) |
| Keyword:
|
Rao-Blackwell theorem |
| Keyword:
|
unbiased estimator |
| MSC:
|
62B99 |
| MSC:
|
62D05 |
| MSC:
|
62F10 |
| MSC:
|
62F86 |
| idZBL:
|
Zbl 1274.62226 |
| idMR:
|
MR1690943 |
| . |
| Date available:
|
2009-09-24T19:24:32Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135278 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Breiman L.: Probability.Addison–Wesley, Reading, MA 1968 Zbl 0753.60001, MR 0229267 |
| Reference:
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[4] Casella G., Berger R. L.: Statistical Inference.Wadsworth & Brooks/Cole, Pacific Grove 1990 Zbl 0699.62001, MR 1051420 |
| Reference:
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[5] Raj D., Khamis S. H.: Some remarks on sampling with replacement.Ann. Math. Statist. 29 (1958), 550–557 Zbl 0086.12404, MR 0094868, 10.1214/aoms/1177706630 |
| Reference:
|
[6] Dudewicz E. J., Mishra S. N.: Modern Mathematical Statistics.Wiley, New York 1988 Zbl 0708.62003, MR 0920168 |
| Reference:
|
[7] López–Díaz M., Gil M. A.: Reversing the order of integration in iterated expectations of fuzzy random variables, and statistical applications.J. Statist. Plann. Inference 74 (1998), 11–29 Zbl 0962.62005, MR 1665118, 10.1016/S0378-3758(98)00100-1 |
| Reference:
|
[8] Lubiano M. A.: Medidas de variación de elementos aleatorios imprecisos.Ph.D. Thesis. Universidad de Oviedo 1999 |
| Reference:
|
[9] Lubiano M. A., Gil M. A.: Estimating the expected value of fuzzy random variables in random samplings from finite populations.Statist. Papers, to appear Zbl 0942.62010, MR 1716519 |
| Reference:
|
[10] Lubiano M. A., Gil M. A., López–Díaz M., López M. T.: The $\vec{\lambda }$-mean squared dispersion associated with a fuzzy random variable.Fuzzy Sets and Systems, to appear |
| Reference:
|
[11] Lubiano M. A., Körner R.: A Generalized Measure of Dispersion for Fuzzy Random Variables.Technical Report, Universidad de Oviedo 1998 |
| Reference:
|
[12] Puri M. L., Ralescu D. A.: Fuzzy random variables.J. Math. Anal. Appl. 114 (1986), 409–422 Zbl 0605.60038, MR 0833596, 10.1016/0022-247X(86)90093-4 |
| Reference:
|
[13] Thompson S. K.: Sampling.Wiley, New York 1992 MR 1193031 |
| . |
