Subsamples of a Set of Symmetric, Independent, Identically Distributed Random Variables which Determine a Set of Typical Values

摘要

Let X = (x sub 1, x sub 2, ..., x sub n) be a set of symmetric, independent, identically distributed random variables. In the case that the variables are not assumed to be identically distributed, there is a group theoretic characterization of the collections of subsamples of X which determine a set of typical values for the parameter 0. In the work it is shown that if the variables are identically distributed, then there is a wider class of collections which determine sets of typical values. The algebraic properties of the elements of this wider class are studied and several theorems are proved. (Author)