Subset selection based on likelihood from uniform and related populations

• Main Author: Chotai, Jayanti
• Format: Others
• Language: English
• Published: Umeå universitet, Matematisk statistik 1979
• Subjects: Subset selection; likelihood ratio; order restrictions; uniform distribution
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-74924

Let π1,  π2, ... π be k (>_2) populations. Let  πi (i = 1, 2, ..., k) be characterized by the uniform distributionon (ai, bi), where exactly one of ai and bi is unknown. With unequal sample sizes, suppose that we wish to select arandom-size subset of the populations containing the one withthe smallest value of 0i = bi - ai. Rule Ri selects πi iff a likelihood-based k-dimensional confidence region for the unknown (01,..., 0k) contains at least one point having 0i as its smallest component. A second rule, R, is derived through a likelihood ratio and is equivalent to that of Barr and Rizvi (1966) when the sample sizes are equal. Numerical comparisons are made. The results apply to the larger class of densities g(z; 0i) = M(z)Q(0i) iff a(0i) < z < b(0i). Extensions to the cases when both ai and bi are unknown and when 0max is of interest are i i indicated. === digitalisering@umu