Denise Steliana Rey
The Informational Order in Ranked Set Sampling Experiments
Preprint series: Mathematica Gottingensis
MSC:
62B15 Theory of statistical experiments
Abstract: The Ranked Set Sampling (RSS) technique was first introduced
by McIntyre (1952) as an efficient alternative to Simple
Random Sampling (SRS) for estimating pasture yields.
We construct a family of statistical experiments which are
based on the RSS procedure. The extreme cases in the family
are given by the SRS of size $n$,
$$SRS:=(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n),\{\otimes_{
i=1}^{n}P_{\theta}^{X}:\,\theta\in\Theta\})$$
and by the RSS experiment without repetition of size $n$,
$$RSS:=(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n),\{\otimes_{
i=1}^{n}P_{\theta}^{X_{[i]}^{n}}:\,\theta\in\Theta\}).$$
We restrict to dominated experiments and establish the
existence or non-existence of Markov kernels between the
experiments in our family. Using the randomization criterion
we decide on the existence or non-existence of the Blackwell
informational order in the family of experiments.

Keywords: Ranked set, information, exhaustivity, decision problem.