A note on approximate confidence limits for the negative binomial model

Four methods of approximating confidence limits for the single negative binomial parameter, P, are outlined and an empirical study is presented. Some remarks on prediction intervals are also included.     

On Response Surface Methodology and its Computer-Assisted Teaching

Since the teaching of response surface methodology involving the steepest ascent (descent) method requires a fair amount of instructor and student time even to complete one analysis, the routine aspects of the method were computerized. Flowcharts that contain the logic of first- and second-order experimentation to reach optimum conditions were also developed.     

Statistical Computing Software Reviews

This section is similar in organization to a Book Review section in other journals; however, software of interest to statisticians is the subject of review here. Emphasis is on software for microcomputers. Programs that operate only in larger mainframe computers will seldom receive review. Normally, producers of programs make a copy of their product available to the Section Editor, who then selects one or more persons to test the product and prepare a review.

Producers of computer software who wish to have their product reviewed are invited to contact the Section Editor, Professor Kenneth Berk, Department of Mathematics, 313 Stevenson Hall, Illinois State University, Normal, IL 61761.

Findings and opinions expressed in every review are solely those of the author. They should not be construed as reflecting endorsement of the product, or opinions held, by the American Statistical Association, nor is any warranty implied about any product reviewed.

STAN, Version II.0. David M. Allen. Available from Statistical Consultants, Inc., 462 E. High Street, Lexington, KY 40508. $300. Reviewed by Peter A. Lachenbruch     

The Role of Statistical Models in the Prediction of Tropical Cyclone Motion

Tropical cyclones (tropical storms, hurricanes, typhoons, etc.) occur over many of the earth's tropical marine areas. Responsibility for tracking and predicting the future course of these storms is assigned to one or more domestic or foreign meteorological services. These services routinely activate a number of statistical and dynamical prediction models as objective guidance preparatory to issuing official forecasts on these storms. In this article, the role of the statistical models in this process is examined.     

Confidence Intervals for the Youden Index and Corresponding Optimal Cut-Point

A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying healthy individuals. The cut-point leading to the index is the optimal cut-point when equal weight is given to sensitivity and specificity. Using the delta method, we present approaches for estimating confidence intervals for the Youden index and corresponding optimal cut-point for normally distributed biomarkers and also those following gamma distributions. We also provide confidence intervals using various bootstrapping methods. A comparison of interval width and coverage probability is conducted through simulation over a variety of parametric situations. Confidence intervals via delta method are shown to have both closer to nominal coverage and shorter interval widths than confidence intervals from the bootstrapping methods.     

Estimation of the Proportion of Defective Units by Using Group Testing Under the Existence of a Threshold of Detection

Group testing procedures, in which groups containing several units are tested without testing each unit, are widely used as cost-effective procedures in estimating the proportion of defective units in a population. A problem arises when we apply these procedures to the detection of genetically modified organisms (GMOs), because the analytical instrument for detecting GMOs has a threshold of detection. If the group size (i.e., the number of units within a group) is large, the GMOs in a group are not detected due to the dilution even if the group contains one unit of GMOs. Thus, most people conventionally use a small group size (which we call conventional group size) so that they can surely detect the existence of defective units if at least one unit of GMOs is included in the group. However, we show that we can estimate the proportion of defective units for any group size even if a threshold of detection exists; the estimate of the proportion of defective units is easily obtained by using functions implemented in a spreadsheet. Then, we show that the conventional group size is not always optimal in controlling a consumer's risk, because such a group size requires a larger number of groups for testing.     

Confidence Intervals for the Hyperparameters in Structural Models

This article deals with the bootstrap as an alternative method to construct confidence intervals for the hyperparameters of structural models. The bootstrap procedure considered is the classical nonparametric bootstrap in the residuals of the fitted model using a well-known approach. The performance of this procedure is empirically obtained through Monte Carlo simulations implemented in Ox. Asymptotic and percentile bootstrap confidence intervals for the hyperparameters are built and compared by means of the coverage percentages. The results are similar but the bootstrap procedure is better for small sample sizes. The methods are applied to a real time series and confidence intervals are built for the hyperparameters.     

Exact bootstrap confidence intervals for regression coefficients in small samples

ABSTRACT

Regression analysis is one of the important tools in statistics to investigate the relationships among variables. When the sample size is small, however, the assumptions for regression analysis can be violated. This research focuses on using the exact bootstrap to construct confidence intervals for regression parameters in small samples. The comparison of the exact bootstrap method with the basic bootstrap method was carried out by a simulation study. It was found that on a very small sample (n ≈ 5) under Laplace distribution with the independent variable treated as random, the exact bootstrap was more effective than the standard bootstrap confidence interval.     

Effects of censoring on the robustness of exponential-based confidence intervals for median lifetime

Statistical procedures for constructing confidence intervals for median lifetime often rest on a distributional assumption for failure times.This paper explores the interplay between censoring levels and robustness for two construction procedures based on exponential lifetime, subject to general right-censoring. Data are simulated from nearby Weibull distributions. As expected, the simulations indicate that when the exponential assumption is not satisfied, observed coverage by the confidence intervals may differ substantially from the specified coverage level. The marked improvement in the robustness properties of the intervals as the level of censoring increases suggests questions for future research.