Multinomial Selection Problem: A Study of BEM and AVC Algorithms

The two well-known and widely used multinomial selection procedures Bechhofor, Elmaghraby, and Morse (BEM) and all vector comparison (AVC) are critically compared in applications related to simulation optimization problems.

Two configurations of population probability distributions in which the best system has the greatest probability p _i of yielding the largest value of the performance measure and has or does not have the largest expected performance measure were studied.

The numbers achieved by our simulations clearly show that none of the studied procedures outperform the other in all situations. The user must take into consideration the complexity of the simulations and the performance measure probability distribution properties when deciding which procedure to employ.

An important discovery was that the AVC does not work in populations in which the best system has the greatest probability p _i of yielding the largest value of the performance measure but does not have the largest expected performance measure.     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

EVVMA and cusum control charts in the presence of correlation

The statistical properties of control charts are usually evaluated under the assumption that the observations from the process are independent. For many processes however, observations which are closely spaced in time will be correlated. This paper considers EWMA and CUSUM control charts for the process mean when the observations are from an AR(1) process with additional random error. This simple model may be a reasonable model for many processes encountered in practice. The ARL and steady state ARL of the EWMA and CUSUM charts are evaluated numerically using an integral equation approach and a Markov chain approach. The numerical results show that correlation can have a significant effect on the properties of these charts. Tables are given to aid in the design of these charts when the observations follow the assumed model.     

On the Alias Method for Generating Random Variables from a Discrete Distribution

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

An Interesting Property of the Sample Mean under a First-Order Autoregressive Model

The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.     

American Statistical Association Style Guide

This article contains the American Statistical Association Style Guide published in The American Statistician volume 40 issue 1, in 1986. To see the current version of the style guide please click here.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

On constructing T 2 control charts for retrospective examination

In this paper we consider the issue of constructing retrospective T ² control chart limits so as to control the overall probability of a false alarm at a specified value. We describe an exact method for constructing the control limits for retrospective examination. We then consider Bonferroni-adjustments to Alt's control limit and to the standard x ² control limit as alternatives to the exact limit since it is computationally cumbersome to find the exact limit. We present the results of some simulation experiments that are carried out to compare the performance of these control limits. The results indicate that the Bonferroni-adjusted Alt's control limit performs better that the Bonferroni-adjusted x ² control limit. Furthermore, it appears that the Bonferroni-adjusted Alt's control limit is more than adequate for controlling the overall false alarm probability at a specified value.