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With reference to the problem of interval estimation of a population mean under model uncertainty, we compare approaches based on robust and empirical statistics via expected lengths of the associated confidence intervals. An explicit expression for confidence intervals arising from a general class of robust statistics is worked out and this is employed to obtain a higher order asymptotic formula for the expected lengths of such intervals. Comparative theoretical results, as well as a simulation study, are then presented.

If the unknown mean of a univariate population is sufficiently close to the value of an initial guess then an appropriate shrinkage estimator has smaller average squared error than the sample mean. This principle has been known for some time, but it does not appear to have found extension to problems of interval estimation. The author presents valid two-sided 95% and 99% "shrinkage" confidence intervals for the mean of a normal distribution. These intervals are narrower than the usual interval based on the Student distribution when the population mean lies in such an "effective interval." A reduction of 20% in the mean width of the interval is possible when the population mean is sufficiently close to the value of the guess. The author also describes a modification to existing shrinkage point estimators of the general univariate mean that enables the effective interval to be enlarged.

PurposeIn order to develop a feasible and efficient method to acquire the long‐run availability of a parallel system with distribution‐free up and down times, the purpose of this paper is to perform the simulation comparisons on the interval estimations of system availability using four bootstrapping methods.Design/methodology/approachBy using four bootstrap methods; standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, bias‐corrected percentile bootstrap (BCPB) confidence interval, and bias‐corrected and accelerated (BCa) confidence interval. A numerical simulation study is carried out in order to demonstrate performance of these proposed bootstrap confidence intervals. Especially, we investigate the accuracy of the four bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative coverage of confidence intervals.FindingsAmong the four bootstrap confidence intervals, the PB method has the largest relative coverage in most situations. That is, the PB method is the best one made by practitioners who want to obtain an efficient interval estimation of availability.Originality/valueIt is the first time that the relative coverage is introduced to evaluate the performance of estimation method, which is more efficient than the existing measures.

In an effort to find accurate alternatives to the usual confidence intervals based on normal approximations, this paper compares four methods of generating second-order accurate confidence intervals for non-standardized and standardized communalities in exploratory factor analysis under the normality assumption. The methods to generate the intervals employ, respectively, the Cornish-Fisher expansion and the approximate bootstrap confidence (ABC), and the bootstrap-t and the bias-corrected and accelerated bootstrap (BC(a)). The former two are analytical and the latter two are numerical. Explicit expressions of the asymptotic bias and skewness of the communality estimators, used in the analytical methods, are derived. A Monte Carlo experiment reveals that the performance of central intervals based on normal approximations is a consequence of imbalance of miscoverage on the left- and right-hand sides. The second-order accurate intervals do not require symmetry around the point estimates of the usual intervals and achieve better balance, even when the sample size is not large. The behaviours of the second-order accurate intervals were similar to each other, particularly for large sample sizes, and no method performed consistently better than the others.

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hajek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.

The problem of estimating nonparametric regression with associated confidence intervals is addressed. It is shown that through appropriate choice of infinite order kernel, it is possible to construct bootstrap confidence intervals which do not require either explicit bias correction or suboptimal levels of smoothing at any stage of the estimation. In particular, it is demonstrated that in this setting, consistent estimates are obtained when both the pilot and final smoothings are estimated at the mean square error optimal bandwidth for estimating the regression. The effectiveness of the method is demonstrated through a small simulation study. © 2008. 78 15 2463 2469 Cited By :5

The conventional confidence interval for the intraclass correlation coefficient assumes equal-tail probabilities. In general, the equal-tail probability interval is biased and other interval procedures should be considered. Unbiased confidence intervals for the intraclass correlation coefficient are readily available. The equal-tail probability and unbiased intervals have exact coverage as they are constructed using the pivotal quantity method. In this article, confidence intervals for the intraclass correlation coefficient are built using balanced and unbalanced one-way random effects models. The expected length of confidence intervals serves as a tool to compare the two procedures. The unbiased confidence interval outperforms the equal-tail probability interval if the intraclass correlation coefficient is small and the equal-tail probability interval outperforms the unbiased interval if the intraclass correlation coefficient is large.

We compared eight nominal 95 per cent confidence intervals for the ratio of two Poisson parameters, both assumed small, on their true coverage (the probability that the interval includes the ratio of Poisson parameters) and median width. The commonly used log-linear interval, justified by asymptotic considerations, provided coverage and relatively narrow intervals, despite small numbers of arrivals. However, the uniform and scores intervals, defined in the text, come very close to providing coverage while providing substantially narrower intervals. These intervals might have practical applications. In a sensitivity analysis, none of the intervals maintained coverage for negative binomial data, indicating that distributional assumptions should be checked before taking our recommendations.

Several large-sample confidence intervals for the ratio of independent binomial proportions are compared in terms of exact coverage probability and width. A non-iterative approximate Bayesian interval is derived and its frequency properties are superior to all of the non-iterative confidence intervals considered. The approximate Bayesian interval, which is very easy to compute, has performance characteristics that are very similar to the computationally intensive score method. Two sample size determination formulas are presented, one for desired absolute precision and the other for desired relative precision.

When estimating risk measures, whether from historical data or by Monte Carlo simulation, it is helpful to have confidence intervals that provide information about statistical uncertainty. We provide asymptotically valid confidence intervals and confidence regions involving value-at-risk (VaR), conditional tail expectation and expected shortfall (conditional VaR), based on three different methodologies. One is an extension of previous work based on robust statistics, the second is a straightforward application of bootstrapping, and we derive the third using empirical likelihood. We then evaluate the small-sample coverage of the confidence intervals and regions in simulation experiments using financial examples. We find that the coverage probabilities are approximately nominal for large sample sizes, but are noticeably low when sample sizes are too small (roughly, less than 500 here). The new empirical likelihood method provides the highest coverage at moderate sample sizes in these experiments. We want to measure the risk of a given portfolio that has random profits at the end of a predetermined investment period. We can sample from the distribution of the portfolio’s profits using Monte Carlo simulation based on a stochastic model of financial markets. Our focus will be on estimating risk measures for our portfolio based on simulated profits and providing information in the form of confidence intervals and regions about the statistical uncertainty of these estimates. We address only this Monte Carlo sampling error in estimating risk, not the model risk that includes errors introduced by using an incorrect model of financial markets and statistical error in estimating the model’s parameters from data. We will emphasize moderate Monte Carlo sample sizes, which are appropriate when

For a normal distribution with known variance, the standard confidence interval of the location parameter is derived from the classical Neyman procedure. When the parameter space is known to be restricted, the standard confidence interval is arguably unsatisfactory. Recent articles have addressed this problem and proposed confidence intervals for the mean of a normal distribution where the parameter space is not less than zero. In this article, we propose a new confidence interval, rp interval, and derive the Bayesian credible interval and likelihood ratio interval for general restricted parameter space. We compare these intervals with the standard interval and the minimax interval. Simulation studies are undertaken to assess the performances of these confidence intervals.

A survey of research by Emanuel Parzen on how quantile functions provide elegant and applicable formulas that unify many statistical methods, especially frequentist and Bayesian confidence intervals and prediction distributions. Section 0: In honor of Ted Anderson's 90th birthday; Section 1: Quantile functions, endpoints of prediction intervals; Section 2: Extreme value limit distributions; Sections 3, 4: Confidence and prediction endpoint function: Uniform ( 0 , θ ) , exponential; Sections: 5, 6: Confidence quantile and Bayesian inference normal parameters μ , σ ; Section 7: Two independent samples confidence quantiles; Section 8: Confidence quantiles for proportions, Wilson's formula. We propose ways that Bayesians and frequentists can be friends!

The paper develops empirical Bayes (EB) confidence intervals for population means with distributions belonging to the natural exponential family-quadratic variance function (NEF-QVF) family when the sample size for a particular population is moderate or large. The basis for such development is to find an interval centred around the posterior mean which meets the target coverage probability asymptotically, and then show that the difference between the coverage probabilities of the Bayes and EB intervals is negligible up to a certain order. The approach taken is Edgeworth expansion so that the sample sizes from the different populations need not be significantly large. The proposed intervals meet the target coverage probabilities asymptotically, and are easy to construct. We illustrate use of these intervals in the context of small area estimation both through real and simulated data. The proposed intervals are different from the bootstrap intervals. The latter can be applied quite generally, but the order of accuracy of these intervals in meeting the desired coverage probability is unknown.

Presenting confidence intervals around means is a common method of expressing uncertainty in data. Loftus and Masson (1994) describe confidence intervals for means in within-subjects designs. These confidence intervals are based on the ANOVA mean squared error. Cousineau (2005) presents an alternative to the Loftus and Masson method, but his method produces confidence intervals that are smaller than those of Loftus and Masson. I show why this is the case and offer a simple correction that makes the expected size of Cousineau confidence intervals the same as that of Loftus and Masson confidence intervals.

We provide a method for obtaining confidence intervals, point estimates, and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way. The method is based on applying the adaptive hypothesis testing procedure of Müller and Schäfer (2001, Biometrics 57, 886-891) to a sequence of dual tests derived from the stage-wise adjusted confidence interval of Tsiatis, Rosner, and Mehta (1984, Biometrics 40, 797-803). In the nonadaptive setting this confidence interval is known to provide exact coverage. In the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage. In general, however, all that can be claimed theoretically is that the coverage is guaranteed to be conservative. Nevertheless, extensive simulation experiments, supported by an empirical characterization of the conditional error function, demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased. No procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting. The methodology is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease.

It is shown how various exact nonparametric inferential procedures can be developed based on record statistics. These include confidence intervals for quantiles, tolerance intervals, outer and inner confidence intervals for quantile intervals, and upper and lower confidence limits for quantile differences. These intervals are all exact and distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that its distribution function is continuous. A data set representing the records of the annual (July 1–June 30) rainfall at Los Angeles Civic Center is used to illustrate the proposed inferential procedures.

Item nonresponse occurs frequently in sample surveys and other approaches to data collection. We consider three different methods of imputation to fill in the missing values in a random sample { Y i , i = 1 , … , n } : (i) mean imputation (M), (ii) random hot deck imputation (R), and (iii) adjusted random hot deck imputation (A). Asymptotic normality of the imputed estimators of the mean μ under M, R and A and the distribution function θ = F ( y ) and qth quantile θ q , under R and A is established, assuming that the values are missing completely at random. This result is used to obtain normal approximation (NA)-based confidence intervals on μ , θ and θ q . In the case of θ q , Woodruff [1952. Confidence intervals for medians and other position measures, J. Amer. Statist. Assoc. 47, 635–646]-type confidence intervals are also obtained under R and A. Empirical log-likelihood ratios for the three cases are also obtained and shown to be asymptotically scaled χ 1 2 . This result is used to obtain asymptotically correct empirical likelihood (EL)-based confidence intervals on μ , θ and θ q . Results of a simulation study on the finite sample performance of NA-based and EL-based confidence intervals are reported. Confidence intervals obtained here do not require identification flags on the imputed values in the data file; only the estimated response rate is needed with the imputed data file. This feature of our method is important because identification flags often may not be provided in practice with the data file due to confidentiality reasons.

In this paper, we investigate various confidence intervals for the risk ratio under inverse sampling (also known as negative binomial sampling). Three existing confidence intervals (namely, the confidence intervals that are based on Fieller's theorem, the delta method and the F-statistic) are reviewed and three new confidence intervals (namely, the score, likelihood ratio and saddlepoint approximation (SA)-based confidence intervals) are developed. Comparative studies among these confidence intervals through Monte Carlo simulations are evaluated in terms of their coverage probabilities and expected interval widths under different settings. Our simulation results suggest that the SA-based confidence interval is generally more appealing. We illustrate these confidence interval construction methods with real data sets from a drug comparison study and a congenital heart disease study.

Three curves are fit to a confidence interval and its estimate. These curves allow a data user to incorporate the variability of the estimation method into further calculations.

Confidence intervals [based on F-distribution and (Z) standard normal distribution] for a linear contrast in intraclass correlation coefficients under unequal family sizes for several populations based on several independent multinormal samples have been proposed. It has been found that the confidence interval based on F-distribution consistently and reliably produced better results in terms of shorter average length of the interval than the confidence interval based on standard normal distribution for various combinations of intraclass correlation coefficient values. The coverage probability of the interval based on F-distribution is competitive with the coverage probability of the interval based on standard normal distribution. The interval based on F-distribution can be used for both small sample and large sample situations. An example with real life data has been presented.

In this paper, we consider the problem wherein one desires to estimate a linear combination of binomial probabilities from k > 2 independent populations. In particular, we create a new family of asymptotic confidence intervals, extending the approach taken by Beal [1987. Asymptotic confidence intervals for the difference between two binomial parameters for use with small samples. Biometrics 73, 941–950] in the two-sample case. One of our new intervals is shown to perform very well when compared to the best available intervals documented in Price and Bonett [2004. An improved confidence interval for a linear function of binomial proportions. Comput. Statist. Data Anal. 45, 449–456]. Furthermore, our interval estimation approach is quite general and could be extended to handle more complicated parametric functions and even to other discrete probability models in stratified settings. We illustrate our new intervals using two real data examples, one from an ecology study and one from a multicenter clinical trial.

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.

Confidence intervals provide a way of reporting an estimate of a population quantile along with some information about the precision of estimates. Some procedures that may be used to obtain estimates of confidence intervals for quantiles in a finite population (most of which are based on resampling) are compared in the paper. A simulation study, based on two different artificial populations, is performed and comparisons of the estimation methods proposed for confidence intervals of population quantiles are made. First Published Online:14 Oct 2010

Asymptotic confidence intervals for the difference between two proportions have been well developed in two-sample correlated binary data. But, the coverage probabilities of such asymptotic confidence intervals are much smaller than the nominal level in small samples, because the asymptotic confidence intervals rely on the large sample theory. The aim of this paper is to construct new confidence intervals whose performance is better than the existing confidence intervals in small samples. Assuming the beta-binomial model, we derive the Edgeworth expansion of the studentized test statistic. Then, we propose new confidence intervals by eliminating the skewness in the Edgeworth expansion. We conduct simulation studies to compare the new confidence intervals with the existing confidence intervals.

This paper presents a generalized variable approach for confidence interval estimation of a common correlation coefficient from several independent samples drawn from bivariate normal populations. This approach can provide one-sided bounds and two-sided confidence intervals with satisfying coverage probabilities regardless of the number of samples, sample sizes and magnitude of the common correlation coefficient while the large sample approach can be very liberal for one-sided bounds. The large sample approach generally performs well for two-sided confidence interval estimation.

In this article we propose a new method for constructing confidence intervals for σα2,σϵ2, and the intraclass correlation ρ==σα2(σα2++σe2) in a two-component mixed-effects linear model. This method is based on an extension of R. A. Fisher's fiducial argument. We conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature. Our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability, as well as shorter average confidence interval lengths overall. We also prove that these fiducial intervals have asymptotically exact frequentist coverage probability. The computations for the proposed procedures are illustrated using real data examples.

The failure probability of a product F(t), and the life time quantile t p are commonly used metrics in reliability applications. Confidence intervals are used to quantify the s-uncertainty of estimators of these two metrics. In practice, a set of pointwise confidence intervals for F(t), or the quantiles t p are often plotted on one graph, which we refer to as pointwise ldquoconfidence bands.rdquo These confidence bands for F(t) or t p can be obtained through s-normal approximation, maximum likelihood, or other procedures. In this paper, we compare s-normal approximation to likelihood methods, and introduce a new procedure to get the confidence intervals for F(t) by inverting the pointwise confidence bands of the quantile t p function. We show why it is valid to interpret the set of pointwise confidence intervals for the quantile function as a set of pointwise confidence intervals for F(t), and vice-versa. Our results also indicate that the likelihood-based pointwise confidence bands have desirable statistical properties, beyond those that were known previously.

Many of the existing methods of finding calibration intervals in simple linear regression rely on the inversion of prediction limits. In this article, we propose an alternative procedure which involves two stages. In the first stage, we find a confidence interval for the value of the explanatory variable which corresponds to the given future value of the response. In the second stage, we enlarge the confidence interval found in the first stage to form a confidence interval called, calibration interval, for the value of the explanatory variable which corresponds to the theoretical mean value of the future observation. In finding the confidence interval in the first stage, we have used the method based on hypothesis testing and percentile bootstrap. When the errors are normally distributed, the coverage probability of resulting calibration interval based on hypothesis testing is comparable to that of the classical calibration interval. In the case of non normal errors, the coverage probability of the calibr...

Simultaneous confidence intervals for multinomial proportions are useful in many areas of science. Since 1964, approximate simultaneous [email protected] confidence intervals have been proposed for multinomial proportions. Although at each point in the parameter space, these confidence sets have asymptotic [email protected] coverage probability, the exact confidence coefficients of these simultaneous confidence intervals for a fixed sample size are unknown before. In this paper, we propose a procedure for calculating exact confidence coefficients for simultaneous confidence intervals of multinomial proportions for any fixed sample size. With this methodology, exact confidence coefficients can be clearly derived, and the point at which the infimum of the coverage probability occurs can be clearly identified.

We consider exact confidence limits obtained from discrete data by inverting a hypothesis test based on a studentized test statistic. We show that these confidence limits (a) are nesting and (b) have greater large sample efficiency than Buehler confidence limits that are required to be nesting.

This article examines several approximate methods to formulate confidence intervals for a single population proportion based on a ranked set sample (RSS). All of the intervals correspond to certain test statistics. That is, the confidence intervals are obtained by inverting the Wald, Wilson, score, and likelihood ratio tests. The Wald and Wilson intervals are based on the asymptotic distributions of two point estimators; the method of moments (MM) estimator and the maximum likelihood (ML) estimator. Continuity corrected versions of these intervals are also discussed. The R statistical software program is used to both calculate and evaluate the proposed intervals. For instance, an actual data set is analyzed for the sake of illustration. Furthermore, a simulation study which compares the intervals via expected widths and coverage probabilities is presented. The study indicates that the confidence intervals derived from the ML methodology generally outperform those based on MM procedures. Additiona...

Let X i,j (1 ≤ i ≤ k, 1 ≤ j ≤ n i ) be independent random variables and for a fixed i, X i,j 's, (1 ≤ j ≤ n i ) be identically distributed random variables with survival function , where α i is a known positive constant. Also, suppose M i and M′ i , respectively, denote the maximum and minimum of the ith sample. This article investigates the nonparametric confidence intervals for an arbitrary quantile of the distribution F and tolerance limits based on these statistics. Various cases have been studied and in each case, the nonparametric confidence intervals are obtained and exact expressions for the confidence coefficients of these confidence intervals are derived. A data set representing the time of successive failures of the air conditioning system on Boeing 720 jet aircraft is used to illustrate the results. Finally, the accuracy of the proposed procedure has been investigated, when α i 's are unknown via a simulation study.

Investigated in this paper is the point estimation and confidence intervals of the treatment efficacy parameter and related secondary parameters in a two-stage adaptive trial. Based on the minimal sufficient statistics, several alternative estimators to the sample averages are proposed to reduce the bias and to improve the precision of estimation. Confidence intervals are constructed using Woodroofe's pivot method. Numerical studies are conducted to evaluate the bias and mean squared error of the estimators and the coverage probability of the confidence intervals.

Summary Confidence intervals for parameters of distributions with discrete sample spaces will be less conservative (i.e. have smaller coverage probabilities that are closer to the nominal level) when defined by inverting a test that does not require equal probability in each tail. However, the P-value obtained from such tests can exhibit undesirable properties, which in turn result in undesirable properties in the associated confidence intervals. We illustrate these difficulties using P-values for binomial proportions and the difference between binomial proportions.

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.

Although it is well known that modern methods of computing confidence intervals (CIs) based on likelihood or simulation have important advantages, normal approximation confidence interval procedures (NACPs) are still widely used, especially in the analysis of censored data. This is because CIs from NACPs are easy to compute and easy to explain. But when the sample size is not large or when there is heavy censoring, the performance of NACPs can be poor. A transformation can be applied to keep CI endpoints from falling outside the parameter space and improve performance, but the degree of improvement (if any) depends on the chosen function. To obtain CIs for distribution probabilities, some seemingly useful transformation functions will cause the estimated variance to blow up in the tails of the distribution and can lead to nonsensical confidence intervals. This article compares different NACPs for distribution probabilities. Our results suggest that an NACP based on a studentized statistic, which we call t...

This paper focuses on the generalization of several software reliability models and the derivation of confidence intervals of reliability assessment measures. First we propose a gamma function model as a generalized model, and discuss how to obtain the confidence intervals from a data set by using a bootstrap scheme when the size of the data set is small. A two-parameter numerical differentiation method is applied to the data set to estimate the model parameters. We also show several numerical illustrations of software reliability assessment.

In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. A simulation study shows that, with discrete populations, it is possible to obtain consistently more accurate confidence levels and shorter intervals compared to the ones reported by the classical method which is implemented in commercial software. More precisely, the best results are obtained by inverting a two-tailed sign test that properly takes into account tied observations. Some real data examples illustrate the use of these confidence intervals.

For a general class of empirical-type likelihoods for the population mean, higher-order asymptotics are developed with a view to characterizing its members which allow, for any given prior, the existence of a confidence interval that has approximately correct posterior as well as frequentist coverage. In particular, it is seen that the usual empirical likelihood always allows such a confidence interval, while many of its variants proposed in the literature do not enjoy this property. An explicit form of the confidence interval is also given. Copyright 2008, Oxford University Press.

In the article, we consider the unbalanced case of the two-way nested random effects model under partial balance. Using the method of generalized confidence intervals (GCIs) introduced in Weeranhandi (1993 1995), a new method is proposed for constructing confidence intervals on linear function of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Hernandez and Burdick (1993), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.

We derive a profile-likelihood confidence interval and a score based confidence interval to estimate the population prevalences, test sensitivities, and test specificities of two conditionally independent diagnostic tests when no gold standard is available. We are motivated by a real-data example on the study of the properties for two fallible diagnostic tests for bovine immunodeficiency virus. We compare the coverage and average width of two new intervals with an interval based on the asymptotic normality of the maximum likelihood estimator and a Bayesian interval estimator via Monte Carlo simulation. We determine that for the parameter configurations considered here, the profile-likelihood, score, and Bayesian intervals all perform adequately in terms of coverage, but overall, the profile-likelihood interval performs best in terms of yielding at least nominal coverage with minimum expected width.

It is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results, as now facilitated by readily available software. However, for a number of effect measures, procedures are either not available or not satisfactory in samples of small to moderate size. In this paper, we describe a general approach for estimating a difference between effect measures, which can also be used to obtain confidence limits for a risk ratio and a lognormal mean. Numerical evaluation shows that this closed-form procedure outperforms existing methods, including the bootstrap.

This paper compares three confidence intervals for the difference between two means when the distributions are non-normal and their variances are unknown. The confidence intervals considered are Welch-Satterthwaite confidence interval, the adaptive interval that incorporates a preliminary test (pre-test) of symmetry for the underlying distributions, and the adaptive interval that incorporates the Shapiro-Wilk test for normality as a pre-test. The adaptive confidence intervals use the Welch-Satterthwaite interval if the pre-test fails to reject symmetry (or normality) for both distributions; otherwise, apply the Welch-Satterthwaite confidence interval to the log-transformed data, then transform the interval back. Our study shows that the adaptive interval with pre-test of symmetry has best coverage among the three intervals considered. Simulation studies show that the adaptive interval with pre-test of symmetry performs as well as the Welch-Satterthwaite interval for symmetric distributions. However, for skewed distributions, the adaptive interval with pre-test of symmetry performs better than the Welch-Satterthwaite interval.

In estimating safety performance, the most common probabilistic structures of the popular statistical models used by transportation safety analysts for modeling motor vehicle crashes are the traditional Poisson and Poisson–gamma (or negative binomial) distributions. Because crash data often exhibit overdispersion, Poisson–gamma models are usually the preferred model. The dispersion parameter of Poisson–gamma models had been assumed to be fixed, but recent research in highway safety has shown that the parameter can potentially be dependent on the covari-ates, especially for flow-only models. Given that the dispersion parameter is a key variable for computing confidence intervals, there is reason to believe that a varying dispersion parameter could affect the computation of confidence intervals compared with confidence intervals produced from Poisson–gamma models with a fixed dispersion parameter. This study evaluates whether the varying dispersion parameter affects the computation of the confidence intervals for the gamma mean (m) and predicted response (y) on sites that have not been used for estimating the predictive model. To accomplish that objective, predictive models with fixed and varying dispersion parameters were estimated by using data collected in California at 537 three-leg rural unsignalized intersections. The study shows that models developed with a varying dispersion parameter greatly influence the confidence intervals of the gamma mean and predictive response. More specifically, models with a varying dispersion parameter usually produce smaller confidence intervals, and hence more precise estimates, than models with a fixed dispersion parameter, both for the gamma mean and for the predicted response. Therefore, it is recommended to develop models with a varying dispersion whenever possible, especially if they are used for screening purposes.

In this paper, we develop methods for generating confidence intervals for the comparison of variability estimates in a mixed-effects model. A generalized confidence interval (GCI) is developed and contrasted to the modified large sample (MLS) method with an adjustment for a fixed effect. The methods are assessed using a computer simulation. Recommendations are provided for selecting an appropriate method. Copyright © 2007 John Wiley & Sons, Ltd.

Background/Aim. It is necessary to decide whether the newly improved methods are better than the standard or reference test or not. To decide whether the new diagnostics test is better than the gold standard test/imperfect standard test, the differences of estimated sensitivity/specificity are calculated with the help of information obtained from samples. However, to generalize this value to the population, it should be given with the confidence intervals. The aim of this study is to evaluate the confidence interval methods developed for the differences between the two dependent sensitivity/specificity values on a clinical application.Materials and Methods. In this study, confidence interval methods like Asymptotic Intervals, Conditional Intervals, Unconditional Interval, Score Intervals, and Nonparametric Methods Based on Relative Effects Intervals are used. Besides, as clinical application, data used in diagnostics study by Dickel et al. (2010) has been taken as a sample.Results. The results belonging to the alternative confidence interval methods for Nickel Sulfate, Potassium Dichromate, and Lanolin Alcohol are given as a table.Conclusion. While preferring the confidence interval methods, the researchers have to consider whether the case to be compared is single ratio or dependent binary ratio differences, the correlation coefficient between the rates in two dependent ratios and the sample sizes.

Traditional two-sample estimation procedures like pooled-t, Welch’s t, and the Wilcoxon-Hodges-Lehmann are often used for skewed data and data inflated with zero values. We investigate how well these work compared to dedicated procedures that consider the specialized nature of the data.