Asymptotically Optimum Estimation of a Probability in Inverse Binomial Sampling under General Loss Functions

Mendo Tomás, Luis (2012). Asymptotically Optimum Estimation of a Probability in Inverse Binomial Sampling under General Loss Functions. "Journal of Statistical Planning and Inference" ; ISSN 0378-3758. https://doi.org/10.1016/j.jspi.2012.03.026.

Description

Title: Asymptotically Optimum Estimation of a Probability in Inverse Binomial Sampling under General Loss Functions
Author/s:
  • Mendo Tomás, Luis
Item Type: Article
Título de Revista/Publicación: Journal of Statistical Planning and Inference
Date: 6 April 2012
ISSN: 0378-3758
Subjects:
Freetext Keywords: Sequential estimation; Asymptotic properties; Minimax estimators; Inverse binomial sampling
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Señales, Sistemas y Radiocomunicaciones
Creative Commons Licenses: Recognition

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Abstract

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.

More information

Item ID: 10749
DC Identifier: http://oa.upm.es/10749/
OAI Identifier: oai:oa.upm.es:10749
DOI: 10.1016/j.jspi.2012.03.026
Deposited by: Dr. Luis Mendo
Deposited on: 08 May 2012 07:34
Last Modified: 20 Apr 2016 18:59
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