On the Rao-Blackwell Theorem for fuzzy random variables

María Asunción Lubiano; María Angeles Gil; Miguel López-Díaz

Kybernetika (1999)

  • Volume: 35, Issue: 2, page [167]-175
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Lubiano, María Asunción, Gil, María Angeles, and López-Díaz, Miguel. "On the Rao-Blackwell Theorem for fuzzy random variables." Kybernetika 35.2 (1999): [167]-175. <http://eudml.org/doc/33419>.

@article{Lubiano1999,
abstract = {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.},
author = {Lubiano, María Asunción, Gil, María Angeles, López-Díaz, Miguel},
journal = {Kybernetika},
keywords = {Rao-Blackwell theorem; unbiased estimator; Rao-Blackwell theorem; unbiased estimator},
language = {eng},
number = {2},
pages = {[167]-175},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the Rao-Blackwell Theorem for fuzzy random variables},
url = {http://eudml.org/doc/33419},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Lubiano, María Asunción
AU - Gil, María Angeles
AU - López-Díaz, Miguel
TI - On the Rao-Blackwell Theorem for fuzzy random variables
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 2
SP - [167]
EP - 175
AB - 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.
LA - eng
KW - Rao-Blackwell theorem; unbiased estimator; Rao-Blackwell theorem; unbiased estimator
UR - http://eudml.org/doc/33419
ER -

References

top
  1. Aumann R. J., 10.1016/0022-247X(65)90049-1, J. Math. Anal. Appl. 12 (1965), 1–12 (1965) Zbl0163.06301MR0185073DOI10.1016/0022-247X(65)90049-1
  2. Bertoluzza C., Corral N., Salas A., On a new class of distances between fuzzy numbers, Mathware Soft Computing 2 (1995), 71–84 (1995) Zbl0887.04003MR1384223
  3. Breiman L., Probability, Addison–Wesley, Reading, MA 1968 Zbl0753.60001MR0229267
  4. Casella G., Berger R. L., Statistical Inference, Wadsworth & Brooks/Cole, Pacific Grove 1990 Zbl0699.62001MR1051420
  5. Raj D., Khamis S. H., 10.1214/aoms/1177706630, Ann. Math. Statist. 29 (1958), 550–557 (1958) Zbl0086.12404MR0094868DOI10.1214/aoms/1177706630
  6. Dudewicz E. J., Mishra S. N., Modern Mathematical Statistics, Wiley, New York 1988 Zbl0708.62003MR0920168
  7. López–Díaz M., Gil M. A., 10.1016/S0378-3758(98)00100-1, J. Statist. Plann. Inference 74 (1998), 11–29 (1998) Zbl0962.62005MR1665118DOI10.1016/S0378-3758(98)00100-1
  8. Lubiano M. A., Medidas de variación de elementos aleatorios imprecisos, Ph.D. Thesis. Universidad de Oviedo 1999 
  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 Zbl0942.62010MR1716519
  10. Lubiano M. A., Gil M. A., López–Díaz M., López M. T., The λ → -mean squared dispersion associated with a fuzzy random variable, Fuzzy Sets and Systems, to appear 
  11. Lubiano M. A., Körner R., A Generalized Measure of Dispersion for Fuzzy Random Variables, Technical Report, Universidad de Oviedo 1998 
  12. Puri M. L., Ralescu D. A., 10.1016/0022-247X(86)90093-4, J. Math. Anal. Appl. 114 (1986), 409–422 (1986) Zbl0605.60038MR0833596DOI10.1016/0022-247X(86)90093-4
  13. Thompson S. K., Sampling, Wiley, New York 1992 MR1193031

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.