Likelihood and statistical evidence in survey sampling
Original version
Statistics in Transition, Vol. 6, No. 1 (2003), pp. 23-31Abstract
A comparison is made of the two concepts, generalized likelihood (from
Bjørnstad, 1996) and Royall's measure of empirical statistical evidence in
prediction problems, here called evidential likelihood, applied to survey
sampling when a population model is assumed. As shown by Bjørnstad
(1996), the likelihood principle based on the generalized likelihood is implied
by conditionality and sufficiency principles, generalizing the fundamental
result from Birnbaum (1962). The main difference between the two likelihood
concepts is that the generalized likelihood is a basis for statistical inference
containing all available statistical information, while the evidential likelihood
concentrates on the empirical evidence per se which does not contain all
available statistical information about the variable to be predicted. One can
regard the evidential likelihood as the sample evidence of the generalized
likelihood, changing the prior distribution of the population total to the
generalized likelihood after the data have been obtained.
Description
Published with permission from The Central Statistical Office of Poland.