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
Nonparametric and parametric subset selection procedures are used in the analysis of state homicide rates (SHRs), for the year 2005 and years 2014-2020, to identify subsets of states that contain the “best” (lowest ...Nonparametric and parametric subset selection procedures are used in the analysis of state homicide rates (SHRs), for the year 2005 and years 2014-2020, to identify subsets of states that contain the “best” (lowest SHR) and “worst” (highest SHR) rates with a prescribed probability. A new Bayesian model is developed and applied to the SHR data and the results are contrasted with those obtained with the subset selection procedures. All analyses are applied within the context of a two-way block design.展开更多
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...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.展开更多
In any parallel system, selecting a component with longer mean lifetime is of interest to the researchers. Hanagal (1997) [1] discussed selection procedures for a two-component system with bivariate exponential (BVE) ...In any parallel system, selecting a component with longer mean lifetime is of interest to the researchers. Hanagal (1997) [1] discussed selection procedures for a two-component system with bivariate exponential (BVE) models. In this paper, the problem of selecting a better component with reference to its mean life time under bivariate Pareto (BVP) models is considered. Three selection procedures based on sample proportions, sample means and maximum likelihood estimators (MLE) are proposed. The probability of correct selection for the proposed procedures is evaluated through Monte Carlo simulation using normal approximation. The asymptotic relative efficiency (ARE) of the proposed procedures is presented to facilitate the evaluation of the performance of procedures.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Nonparametric and parametric subset selection procedures are used in the analysis of state homicide rates (SHRs), for the year 2005 and years 2014-2020, to identify subsets of states that contain the “best” (lowest SHR) and “worst” (highest SHR) rates with a prescribed probability. A new Bayesian model is developed and applied to the SHR data and the results are contrasted with those obtained with the subset selection procedures. All analyses are applied within the context of a two-way block design.
文摘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.
文摘In any parallel system, selecting a component with longer mean lifetime is of interest to the researchers. Hanagal (1997) [1] discussed selection procedures for a two-component system with bivariate exponential (BVE) models. In this paper, the problem of selecting a better component with reference to its mean life time under bivariate Pareto (BVP) models is considered. Three selection procedures based on sample proportions, sample means and maximum likelihood estimators (MLE) are proposed. The probability of correct selection for the proposed procedures is evaluated through Monte Carlo simulation using normal approximation. The asymptotic relative efficiency (ARE) of the proposed procedures is presented to facilitate the evaluation of the performance of procedures.
