Conditional probability of correct selection under the continuum partition with applications
Conditional probability of correct selection under the continuum partition with applications
The problem of selecting the best population from among a finite number of populations in the presence of uncertainty is a problem one faces in many scientific investigations, and has been studied extensively, Many selection procedures have been derived for different selection goals. However, most of these selection procedures, being frequentist in nature, don't tell how to incorporate the information in a particular sample to give a data-dependent measure of correct selection achieved for this particular sample. They often assign the same decision and probability of correct selection for two different sample values, one of which actually seems intuitively much more conclusive than the other. The methodology of conditional inference offers an approach which achieves both frequentist interpret ability and a data-dependent measure of conclusiveness. By partitioning the sample space into a family of subsets, the achieved probability of correct selection is computed by conditioning on which subset the sample falls in. In this paper, the partition considered is the so called continuum partition, while the selection rules are both the fixed-size and random-size subset selection rules. Under the distributional assumption of being monotone likelihood ratio, results on least favourable configuration and alpha-correct selection are established. These results are not only useful in themselves, but also are used to design a new sequential procedure with elimination for selecting the best of k Binomial populations. Comparisons between this new procedure and some other sequential selection procedures with regard to total expected sample size and some risk functions are carried out by simulations.
selection, conditional inference, monotone likelihood ratio, sequential procedure, expected sample size, risk
1085-1111
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
1993
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Liu, Wei
(1993)
Conditional probability of correct selection under the continuum partition with applications.
Communications in Statistics: Theory and Methods, 22 (4), .
(doi:10.1080/03610928308831075).
Abstract
The problem of selecting the best population from among a finite number of populations in the presence of uncertainty is a problem one faces in many scientific investigations, and has been studied extensively, Many selection procedures have been derived for different selection goals. However, most of these selection procedures, being frequentist in nature, don't tell how to incorporate the information in a particular sample to give a data-dependent measure of correct selection achieved for this particular sample. They often assign the same decision and probability of correct selection for two different sample values, one of which actually seems intuitively much more conclusive than the other. The methodology of conditional inference offers an approach which achieves both frequentist interpret ability and a data-dependent measure of conclusiveness. By partitioning the sample space into a family of subsets, the achieved probability of correct selection is computed by conditioning on which subset the sample falls in. In this paper, the partition considered is the so called continuum partition, while the selection rules are both the fixed-size and random-size subset selection rules. Under the distributional assumption of being monotone likelihood ratio, results on least favourable configuration and alpha-correct selection are established. These results are not only useful in themselves, but also are used to design a new sequential procedure with elimination for selecting the best of k Binomial populations. Comparisons between this new procedure and some other sequential selection procedures with regard to total expected sample size and some risk functions are carried out by simulations.
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Published date: 1993
Keywords:
selection, conditional inference, monotone likelihood ratio, sequential procedure, expected sample size, risk
Organisations:
Statistical Sciences Research Institute
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Local EPrints ID: 381071
URI: http://eprints.soton.ac.uk/id/eprint/381071
ISSN: 0361-0926
PURE UUID: 910f5e4c-2da7-4a66-9e8e-7e81b5264ecd
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Date deposited: 05 Oct 2015 11:01
Last modified: 15 Mar 2024 02:43
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