Abstract :
Suppose X = (X
1
; ; X
p
); (p 2); where X
represents the mean of a random sample of size
n
i
drawn from binomial bin(1;
i
i
) population. Assume the parameters
are unknown
and the populations bin(1;
1
); ; bin(1;
p
1
; ;
) are independent. A subset of random size is
selected using Guptaʹs (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 riskunbiased
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.
p
