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On Performance Characteristics of a Nonparametric Subset Selection Procedure with a Small Randomized Block Experimental Design

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Applied Mathematics 2024年第9期15卷 630-650页

作者： Gary C. McDonald sajidah alsaeed Department of Mathematics and Statistics Oakland University Rochester MI USA

This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e. , that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.

关键词： Rank Statistics Least Favorable Configuration Probability of Correct Selection Slippage Configuration Equal Spaced Configuration Counterexample Configuration

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Comparison of Block Design Nonparametric Subset Selection Rules Based on Alternative Scoring Rules

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Applied Mathematics 2024年第5期15卷 355-389页

作者： Gary C. McDonald sajidah alsaeed Department of Mathematics and Statistics Oakland University Rochester MI USA

This article compares the size of selected subsets using nonparametric subset selection rules with two different scoring rules for the observations. The scoring rules are based on the expected values of order statistics of the uniform distribution (yielding rank values) and of the normal distribution (yielding normal score values). The comparison is made using state motor vehicle traffic fatality rates, published in a 2016 article, with fifty-one states (including DC as a state) and over a nineteen-year period (1994 through 2012). The earlier study considered four block design selection rules—two for choosing a subset to contain the “best” population (i.e., state with lowest mean fatality rate) and two for the “worst” population (i.e., highest mean rate) with a probability of correct selection chosen to be 0.90. Two selection rules based on normal scores resulted in selected subset sizes substantially smaller than corresponding rules based on ranks (7 vs. 16 and 3 vs. 12). For two other selection rules, the subsets chosen were very close in size (within one). A comparison is also made using state homicide rates, published in a 2022 article, with fifty states and covering eight years. The results are qualitatively the same as those obtained with the motor vehicle traffic fatality rates.

关键词： Order Statistics Rank Scoring Methods Probability of a Correct Selection Subset Size Motor Vehicle Traffic Fatality Rates Homicide Rates Asymptotic Distributions

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