scholarly journals On an Inequality That Implies the Lower Bound Formula for the Probability of Correct Selection in the Levin-Robbins-Leu Family of Sequential Binomial Subset Selection Procedures

2013 ◽  
Vol 32 (4) ◽  
pp. 404-427 ◽  
Author(s):  
Bruce Levin ◽  
Cheng-Shiun Leu
Keyword(s):  
Lower Bound ◽  
Subset Selection ◽  
Correct Selection ◽  
Selection Procedures ◽  
Probability Of Correct Selection

Fixed-Confidence, Fixed-Tolerance Guarantees for Ranking-and-Selection Procedures

2021 ◽  
Vol 31 (2) ◽  
pp. 1-33
Author(s):  
David J. Eckman ◽  
Shane G. Henderson
Keyword(s):  
Sufficient Conditions ◽  
Subset Selection ◽  
Ranking And Selection ◽  
Correct Selection ◽  
Selection Procedures ◽  
Indifference Zone ◽  
Second Best ◽  
Probability Of Correct Selection ◽  
Statistical Ranking ◽  
Ranking And Selection Procedures

Ever since the conception of the statistical ranking-and-selection (R8S) problem, a predominant approach has been the indifference-zone (IZ) formulation. Under the IZ formulation, R8S procedures are designed to provide a guarantee on the probability of correct selection (PCS) whenever the performance of the best system exceeds that of the second-best system by a specified amount. We discuss the shortcomings of this guarantee and argue that providing a guarantee on the probability of good selection (PGS)—selecting a system whose performance is within a specified tolerance of the best—is a more justifiable goal. Unfortunately, this form of fixed-confidence, fixed-tolerance guarantee has received far less attention within the simulation community. We present an overview of the PGS guarantee with the aim of reorienting the simulation community toward this goal. We examine numerous techniques for proving the PGS guarantee, including sufficient conditions under which selection and subset-selection procedures that deliver the IZ-inspired PCS guarantee also deliver the PGS guarantee.

Algorithm for Calculating the Initial Sample Size in a Fully Sequential Ranking and Selection Procedure

2020 ◽  
Vol 37 (03) ◽  
pp. 2050015
Author(s):  
Ruijing Wu ◽  
Shaoxuan Liu ◽  
Zhenyang Shi
Keyword(s):  
Sample Size ◽  
Selection Procedure ◽  
Total Sample ◽  
Ranking And Selection ◽  
Correct Selection ◽  
Initial Sample ◽  
Selection Procedures ◽  
Probability Of Correct Selection ◽  
Ranking And Selection Procedures ◽  
The Impact

In some fully sequential ranking and selection procedures, such as the KN procedure and Rinott’s procedure, some initial samples must be taken to estimate the variance. We analyze the impact of the initial sample size (ISS) on the total sample size and propose an algorithm to calculate the ISS in this type of procedure. To better illustrate our approach, we implement this algorithm on the KN procedure and propose the KN-ISS procedure. Comprehensive numerical experiments reveal that this procedure can significantly improve the efficiency compared with the KN procedure and still deliver the desired probability of correct selection.

scholarly journals Finding Points in General Position

2017 ◽  
Vol 27 (04) ◽  
pp. 277-296 ◽  
Author(s):  
Vincent Froese ◽  
Iyad Kanj ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Lower Bound ◽  
General Position ◽  
Subset Selection ◽  
Selection Problem ◽  
Fixed Parameter Tractability ◽  
Maximum Cardinality ◽  
Exponential Time ◽  
Running Time ◽  
Fixed Parameter ◽  
Set Of Points

We study the General Position Subset Selection problem: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and present several fixed-parameter tractability results for the problem as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.

scholarly journals A Procedure For Selecting A Best Multinomial Distribution With Application To Population Income Mobility

2011 ◽  
Vol 10 (1) ◽  
Author(s):  
Saad T. Bakir
Keyword(s):  
Linear Combination ◽  
Multinomial Distribution ◽  
Correct Selection ◽  
Income Mobility ◽  
Probability Of Correct Selection ◽  
The One ◽  
Economics Of Happiness

A procedure is developed for selecting a subset which is asserted to contain the “best” of several multinomial populations with a pre-assigned probability of correct selection. According to a pre-chosen linear combination of the multinomial cell probabilities, the “best” population is defined to be the one with the highest such linear combination. As an illustration, the proposed procedure is applied to data relating to the economics of happiness and population income mobility.

Subset selection procedures

2009 ◽  
Vol 3 (4) ◽  
pp. 202-210 ◽  
Author(s):  
E J Chen
Keyword(s):  
Subset Selection ◽  
Selection Procedures

Selecting the Best Alternative Based on Its Quantile

2020 ◽  
Author(s):  
Demet Batur ◽  
F. Fred Choobineh
Keyword(s):  
Value At Risk ◽  
Decision Makers ◽  
Correct Selection ◽  
Zone Size ◽  
Indifference Zone ◽  
Probability Of Correct Selection ◽  
A Value ◽  
Conscious Decision ◽  
Target Probability ◽  
Sequential Procedures

A value-at-risk, or quantile, is widely used as an appropriate investment selection measure for risk-conscious decision makers. We present two quantile-based sequential procedures—with and without consideration of equivalency between alternatives—for selecting the best alternative from a set of simulated alternatives. These procedures asymptotically guarantee a user-defined target probability of correct selection within a prespecified indifference zone. Experimental results demonstrate the trade-off between the indifference-zone size and the number of simulation iterations needed to render a correct selection while satisfying a desired probability of correct selection.

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