Subset selection procedures based on sample ranges

Abstract

This paper is concerned with subset selection procedures which are based on the sample ranges. The k Independent populations are assumed ordered by unknown scale parameters and it is desired to choose a (small nonempty) subset of these populations with a probabilistic guarantee that the population with the smallest scale parameter is contained in the chosen subset. Location parameters can be either known or unknown since the proposed rules are translation invariant. A class of selection procedures based on the sample ranges from n independent observations are considered and the probability of a correct selection investigated. The constants required to actually implement a particular member of this class of procedures are tabulated for selected values of k and n assuming the underlying populations are normally distributed. An expression for the expected subset size is derived and its maximum value investigated with particular emphasis on normal distributions. A Monte Carlo comparison is made between the new procedure based on sample ranges and a procedure proposed by Gupta and Sobel (1962a) based on the sample variances.

Keywords:

• probability of a correct selection
• expected subset size
• percentage points
• adaptive quadrature
• variance procedure
• Monte Carlo simulations