Estimating the Average Worth of a Subset Selected from Binomial Populations
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Authors
Riyadh Al-Mosawi
- Department of Mathematics, Thiqar University, Thiqar, Iraq
Abstract
Suppose \(\overline{X}=(\overline{X}_1,...\overline{X}_p), (p\geq 2)\); where \(\overline{X}_i\)represents the mean of a random sample of size
ni drawn from binomial \(bin(1,\theta_i)\) population. Assume the parameters \(\theta_1,...,\theta_p\) are unknown
and the populations \(bin(1,\theta_1),...,bin(1,\theta_p)\) are independent. A subset of random size is
selected using Gupta's (Gupta, S. S. (1965). On some multiple decision(selection and ranking)
rules. Technometrics 7,225-245) subset selection procedure. In this paper, we estimate of the
average worth of the parameters for the selected subset under squared error loss and normalized
squared error loss functions. First, we show that neither the unbiased estimator nor the risk-
unbiased estimator of the average worth (corresponding to the normalized squared error loss
function) exist based on a single-stage sample. Second, when additional observations are
available from the selected populations, we derive an unbiased and risk-unbiased estimators of
the average worth and also prove that the natural estimator of the average worth is positively
biased. Finally, the bias and risk of the natural, unbiased and risk-unbiased estimators are
computed and compared using Monti Carlo simulation method.
Share and Cite
ISRP Style
Riyadh Al-Mosawi, Estimating the Average Worth of a Subset Selected from Binomial Populations, Journal of Mathematics and Computer Science, 3 (2011), no. 2, 236--245
AMA Style
Al-Mosawi Riyadh, Estimating the Average Worth of a Subset Selected from Binomial Populations. J Math Comput SCI-JM. (2011); 3(2):236--245
Chicago/Turabian Style
Al-Mosawi, Riyadh. "Estimating the Average Worth of a Subset Selected from Binomial Populations." Journal of Mathematics and Computer Science, 3, no. 2 (2011): 236--245
Keywords
- binomial populations
- selected subset
- average worth estimation
MSC
References
-
[1]
R. Al-Mosawi, P. Vellaisamy, A. Shanubhogue, Risk-Unbiased estimation of the selected subset of Poisson populations, Journal of Indian Statistical Association, Vol. 49, (2011)
-
[2]
R. R. Al-Mosawi, A. Shanubhogue, P. Vellaisamy, Average worth estimation of the selected subset of Poisson populations, Statistitcs, 46 (2012), 813--831
-
[3]
J. D. Gibbons, I. Olkin, M. Sobel, Selecting and ordering populations: a new statistical methodology.Society for Industrial and Applied Mathematics (SIAM), SIAM, Philadelphia (1999)
-
[4]
S. S. Gupta, On some multiple decision (selection and ranking) rules, Technometrics, 7 (1965), 225--245
-
[5]
S. S. Gupta, S. Panchapakesan, Multiple decision procedures: theory and methodology of selection and ranking populations. Society for Industrial and Applied Mathematics (SIAM), SIAM, Philadelphia (2002)
-
[6]
S. Jeyarathnam, S. Panchapakesan, An estimation problem relating to subset selection for normal populations, Design of Experiments: Ranking and Selection (Technical rept.), New York (1983)
-
[7]
S. Jeyarathnam, S. Panchapakesan, Estimation after subset selection from exponential populations, Communications in Statistics-Theory and Methods, 15 (1986), 3459--3473
-
[8]
S. Kumar, A. K. Mahapatra, P. Vellaisamy, Relaibility estimation of the selected exponential populations, Statistics & Probability Letters, 52 (2009), 305--318
-
[9]
E. L. Lehmann, G. Casella, Theory of point estimation, Springer-Verlag, New York (1998)
-
[10]
P. Vellaisamy, Average worth and simulatneous estimation of the selected subset, Ann. Inst. Statist. Math., 44 (1992), 551--562
-
[11]
P. Vellaisamy, On UMVUE estimation following selection, Comm. Statist--Theory Methods, 22 (1993), 1031--1043
-
[12]
P. Vellaisamy, Simultaneous estimation of the selected subset of uniform populations, J. Appl. Statist.Sci., 5 (1996), 39--46
-
[13]
P. Vellaisamy, R. R. Al-Mosawi, Simultaneous estimation of Poisson means of the selected subset, J. Statist. Plann. Infer., 140 (2010), 3355--3364