Better nonparametric bootstrap confidence intervals for the correlation coefficient

We respond to criticism leveled at bootstrap confidence intervals for the correlation coefficient by recent authors by arguing that in the correlation coefficient case, non–standard methods should be employed. We propose two such methods. The first is a bootstrap coverage coorection algorithm using iterated bootstrap techniques (Hall, 1986; Beran, 1987a; Hall and Martin, 1988) applied to ordinary percentile–method intervals (Efron, 1979), giving intervals with high coverage accuracy and stable lengths and endpoints. The simulation study carried out for this method gives results for sample sizes 8, 10, and 12 in three parent populations. The second technique involves the construction of percentile–t bootstrap confidence intervals for a transformed correlation coefficient, followed by an inversion of the transformation, to obtain “transformed percentile–t” intervals for the correlation coefficient. In particular, Fisher's z–transformation is used, and nonparametric delta method and jackknife variance estimates are used to Studentize the transformed correlation coefficient, with the jackknife–Studentized transformed percentile–t interval yielding the better coverage accuracy, in general. Percentile–t intervals constructed without first using the transformation perform very poorly, having large expected lengths and erratically fluctuating endpoints. The simulation study illustrating this technique gives results for sample sizes 10, 15 and 20 in four parent populations. Our techniques provide confidence intervals for the correlation coefficient which have good coverage accuracy (unlike ordinary percentile intervals), and stable lengths and endpoints (unlike ordinary percentile–t intervals).     

Replication: Belief elicitation with quadratic and binarized scoring rules

Researchers increasingly elicit beliefs to understand the underlying motivations of decision makers. Two commonly used methods are the quadratic scoring rule (QSR) and the binarized scoring rule (BSR). Hossain and Okui (2013) use a within-subject design to evaluate the performance of these two methods in an environment where subjects report probabilistic beliefs over binary outcomes with objective probabilities. In a near replication of their study, we show that their results continue to hold with a between-subject design. This is an important validation of the BSR given that researchers typically implement only one method to elicit beliefs. In favor of the BSR, reported beliefs are less accurate under the QSR than the BSR. Consistent with theoretical predictions, risk-averse subjects distort their reported beliefs under the QSR.     

Precision,bias, and uncertainty for state population forecasts: an exploratory analysis of time series models

Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.     

Assessing the Accuracy of Self-Reported Data: an Evaluation of the Toxics Release Inventory

Self-reported regulatory data are hard to verify. This article compares air emissions reported by plants in the Toxics Release Inventory with chemical concentration levels measured by EPA pollution monitors. We find that the large drops in air emissions reported by firms in the TRI are not always matched by similar reductions in measured concentrations from EPA monitors. When the first digits of the monitored chemical concentrations follow a monotonically decreasing distribution, we expect (via Benford's Law) a similar distribution of first digits for the TRI data. For lead and nitric acid the self-reported data do not follow the expected first digit pattern. This suggests that for these two heavily regulated chemicals plants are not reporting accurate estimates of their air emissions. JEL Classification K32, Q53     

Conditional Maximum Likelihood and Interval Estimation for Two Weibull Populations under Joint Type-II Progressive Censoring

Comparative lifetime experiments are important when the object of a study is to determine the relative merits of two competing duration of life products. This study considers the interval estimation for two Weibull populations when joint Type-II progressive censoring is implemented. We obtain the conditional maximum likelihood estimators of the two Weibull parameters under this scheme. Moreover, simultaneous approximate confidence region based on the asymptotic normality of the maximum likelihood estimators are also discussed and compared with two Bootstrap confidence regions. We consider the behavior of probability of failure structure with different schemes. A simulation study is performed and an illustrative example is also given.     

Stein type confidence interval of the disturbance variance in a linear regression model with multivariate student-t distributed errors

This paper considers the interval estimation of the disturbance variance in a linear regression model with multivariate Student-t errors. The distribution function of the Stein type estimator under multivariate Student-t errors is derived, and the coverage probability of the Stein type confidence interval which is constructed under the normality assumption is numerically calculated under the multivariate Student-t distribution. It is shown that the coverage probability of the Stein type confidence interval is sometimes much smaller than the nominal level, and that it is larger than that of the usual confidence interval in almost all cases. For the case when it is known that errors have a multivariate Student-t distribution, sufficient conditions under which the Stein type confidence interval improves on the usual confidence interval are given, and the coverage probability of the stein type confidence interval is numerically evaluated.     

Some Properties of the Exact and Score Methods for Binomial Proportion and Sample Size Calculation

In this article, we point out some interesting relations between the exact test and the score test for a binomial proportion p. Based on the properties of the tests, we propose some approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power. Sample sizes required for the tests are tabulated for various values of p to attain a power of 0.80 at level 0.05. We also propose approximate and exact methods of computing sample sizes needed to construct confidence intervals with a given precision. Using the proposed exact methods, sample sizes required to construct 95% confidence intervals with various precisions are tabulated for p = .05(.05).5. The approximate methods for computing sample sizes for score confidence intervals are very satisfactory and the results coincide with those of the exact methods for many cases.     

Challenges in telemedicine equivalence studies

As the number of telemedicine programs continues to grow, the accuracy of diagnosis over interactive televideo is a central concern. Although investigators have begun to address diagnostic equivalency in telehealth clinics, few published studies reflect strong research design. The two presented telehealth programs completed randomized controlled trials in real-world clinical settings that addressed some of the methodologic shortcomings of prior studies. Diagnostic equivalency studies were completed across five telehealth specialty clinics: physical therapy, speech therapy, ambulatory pediatrics, child psychiatry, and developmental disabilities services. The two research teams encountered similar decision points in designing and implementing the equivalency protocols. This article addresses methodologic issues in choosing design, participants, technology, and evaluation measures. Although the paper focuses on interactive televideo, the issues raised are pertinent across telehealth technologies.     

Quantifying Community Resilience Using Hierarchical Bayesian Kernel Methods: A Case Study on Recovery from Power Outages

The ability to accurately measure recovery rate of infrastructure systems and communities impacted by disasters is vital to ensure effective response and resource allocation before, during, and after a disruption. However, a challenge in quantifying such measures resides in the lack of data as community recovery information is seldom recorded. To provide accurate community recovery measures, a hierarchical Bayesian kernel model (HBKM) is developed to predict the recovery rate of communities experiencing power outages during storms. The performance of the proposed method is evaluated using cross‐validation and compared with two models, the hierarchical Bayesian regression model and the Poisson generalized linear model. A case study focusing on the recovery of communities in Shelby County, Tennessee after severe storms between 2007 and 2017 is presented to illustrate the proposed approach. The predictive accuracy of the models is evaluated using the log‐likelihood and root mean squared error. The HBKM yields on average the highest out‐of‐sample predictive accuracy. This approach can help assess the recoverability of a community when data are scarce and inform decision making in the aftermath of a disaster. An illustrative example is presented demonstrating how accurate measures of community resilience can help reduce the cost of infrastructure restoration.