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 statisti...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.展开更多
This article constructs statistical selection procedures for exponential populations that may differ in only the threshold parameters. The scale parameters of the populations are assumed common and known. The independ...This article constructs statistical selection procedures for exponential populations that may differ in only the threshold parameters. The scale parameters of the populations are assumed common and known. The independent samples drawn from the populations are taken to be of the same size. The best population is defined as the one associated with the largest threshold parameter. In case more than one population share the largest threshold, one of these is tagged at random and denoted the best. Two procedures are developed for choosing a subset of the populations having the property that the chosen subset contains the best population with a prescribed probability. One procedure is based on the sample minimum values drawn from the populations, and another is based on the sample means from the populations. An “Indifference Zone” (IZ) selection procedure is also developed based on the sample minimum values. The IZ procedure asserts that the population with the largest test statistic (e.g., the sample minimum) is the best population. With this approach, the sample size is chosen so as to guarantee that the probability of a correct selection is no less than a prescribed probability in the parameter region where the largest threshold is at least a prescribed amount larger than the remaining thresholds. Numerical examples are given, and the computer R-codes for all calculations are given in the Appendices.展开更多
文摘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.
文摘This article constructs statistical selection procedures for exponential populations that may differ in only the threshold parameters. The scale parameters of the populations are assumed common and known. The independent samples drawn from the populations are taken to be of the same size. The best population is defined as the one associated with the largest threshold parameter. In case more than one population share the largest threshold, one of these is tagged at random and denoted the best. Two procedures are developed for choosing a subset of the populations having the property that the chosen subset contains the best population with a prescribed probability. One procedure is based on the sample minimum values drawn from the populations, and another is based on the sample means from the populations. An “Indifference Zone” (IZ) selection procedure is also developed based on the sample minimum values. The IZ procedure asserts that the population with the largest test statistic (e.g., the sample minimum) is the best population. With this approach, the sample size is chosen so as to guarantee that the probability of a correct selection is no less than a prescribed probability in the parameter region where the largest threshold is at least a prescribed amount larger than the remaining thresholds. Numerical examples are given, and the computer R-codes for all calculations are given in the Appendices.
