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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 3, Fasc. 1,
pages 1 - 17
 

COMPARISON OF SOME STATISTICAL EXPERIMENTS ASSOCIATED WITH SAMPLING PLANS

Erik Torgersen

Abstract: Some experiments occurring in sampling theory may be described as follows:

Consider a finite population F and a characteristic of interest which, with varying amount (value, degree, etc.), is possessed by all individuals in F . Let h(i) be the amount of this characteristic for an individual i .

It is known that h belongs to some set Q of functions on F .

Let a be a sampling plan, i.e. a probability distribution on the set of finite sequences of elements from F . If this sampling plan is used and if the characteristics of sampled individuals are determined without error, then the outcome

x = ((i,h(i)),...,(i,h(i )))
      1   1      n   n
is obtained with probability a(i1,...,in).

Let Ea  denote the experiment obtained by observing x and assume that Q is not too small. Then Ea1  is at least as informative as Ea2  if and only if the sampled subset under a2  is ”stochastically contained” in the sampled subset under a1. Using the theory of comparison of statistical experiments we shall here discuss this and other related results.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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