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Stute (1993, Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis 45, 89–103) proposed a new method to estimate regression models with a censored response variable using least squares and showed the consistency and asymptotic normality for his estimator. This article proposes a new bootstrap-based methodology that improves the performance of the asymptotic interval estimation for the small sample size case. Therefore, we compare the behavior of Stute's asymptotic confidence interval with that of several confidence intervals that are based on resampling bootstrap techniques. In order to build these confidence intervals, we propose a new bootstrap resampling method that has been adapted for the case of censored regression models. We use simulations to study the improvement the performance of the proposed bootstrap-based confidence intervals show when compared to the asymptotic proposal. Simulation results indicate that, for the new proposals, coverage ...

Exact confidence intervals for variances rely on normal distribution assumptions. Alternatively, large-sample confidence intervals for the variance can be attained if one estimates the kurtosis of the underlying distribution. The method used to estimate the kurtosis has a direct impact on the performance of the interval and thus the quality of statistical inferences. In this paper the author considers a number of kurtosis estimators combined with large-sample theory to construct approximate confidence intervals for the variance. In addition, a nonparametric bootstrap resampling procedure is used to build bootstrap confidence intervals for the variance. Simulated coverage probabilities using different confidence interval methods are computed for a variety of sample sizes and distributions. A modification to a conventional estimator of the kurtosis, in conjunction with adjustments to the mean and variance of the asymptotic distribution of a function of the sample variance, improves the resulting coverage va...

This paper provides asymptotic simultaneous confidence intervals for a success probability and intraclass correlation of the beta-binomial model, based on the maximum likelihood estimator approach. The coverage probabilities of those intervals are evaluated. An application to screening mammography is presented as an example. The individual and simultaneous confidence intervals for sensitivity and specificity and the corresponding intraclass correlations are investigated. Two additional examples using influenza data and sex ratio data among sibships are also considered, where the individual and simultaneous confidence intervals are provided.

The magnitude of light intensity of many stars varies over time in a periodic way. Therefore, estimation of period and making inference about this parameter are of great interest in astronomy. The periodogram can be used to estimate period, properly. Bootstrap confidence intervals for period suggested here, are based on using the periodogram and constructed by percentile-t methods. We prove that the equal-tailed percentile-t bootstrap confidence intervals for period have an error of order n −1. We also show that the symmetric percentile-t bootstrap confidence intervals reduce the error to order n −2, and hence have a better performance. Finally, we assess the theoretical results by conducting a simulation study, compare the results with the coverages of percentile bootstrap confidence intervals for period and then analyze a real data set related to the eclipsing system R Canis Majoris collected by Shiraz Biruni Observatory.

A Bayesian approach is considered for the interval estimation of a binomial proportion in doubly sampled data. The coverage probability and the expected width of the Bayesian confidence interval are compared with likelihood-related confidence intervals. It is shown that a hierarchical Bayesian approach provides relatively simple and effective confidence intervals. In addition, it is shown that Agresti–Coull type confidence interval, discussed by Lee and Choi (2009) , can be justified by the Bayesian framework.

The method of tail functions is applied to confidence estimation of the exponential mean in the presence of prior information. It is shown how the “ordinary” confidence interval can be generalized using a class of tail functions and then engineered for optimality, in the sense of minimizing prior expected length over that class, whilst preserving frequentist coverage. It is also shown how to derive the globally optimal interval, and how to improve on this using tail functions when criteria other than length are taken into consideration. Probabilities of false coverage are reported for some of the intervals under study, and the theory is illustrated by application to confidence estimation of a reliability coefficient based on some survival data.

In this paper, a new design-oriented two-stage two-sided simultaneous confidence intervals, for comparing several exponential populations with control population in terms of location parameters under heteroscedasticity, are proposed. If there is a prior information that the location parameter of k exponential populations are not less than the location parameter of control population, one-sided simultaneous confidence intervals provide more inferential sensitivity than two-sided simultaneous confidence intervals. But the two-sided simultaneous confidence intervals have advantages over the one-sided simultaneous confidence intervals as they provide both lower and upper bounds for the parameters of interest. The proposed design-oriented two-stage two-sided simultaneous confidence intervals provide the benefits of both the two-stage one-sided and two-sided simultaneous confidence intervals. When the additional sample at the second stage may not be available due to the experimental budget shortage or other fac...

An estimation of confidence intervals is essential to calculate uncertainty for greenhouse gases inventory. It is generally assumed that the population has a normal distribution for the confidence interval of parameters. However, in case data distribution is asymmetric, like nonnormal distribution or positively skewness distribution, the traditional estimation method of confidence intervals is not adequate. This study compares two estimation methods of confidence interval; parametric and non-parametric method for exponential distribution as an asymmetric distribution. In simulation study, coverage probability, confidence interval length, and relative bias for the evaluation of the computed confidence intervals. As a result, the chi-square method and the standardized t-bootstrap method are better methods in parametric methods and non-parametric methods respectively.

A confidence interval for the probability of detection across laboratories (LPOD) for qualitative methods, described in the AOAC INTERNATIONAL guidelines for validation of microbiological methods for food and environmental surfaces, is considered. It is demonstrated that under certain conditions, the observed confidence of this confidence interval can be rather low, so that statistical minimum requirements are not fulfilled. A new profile likelihood confidence interval based on a latent random laboratory effect approach is proposed. Observed confidence levels for this confidence interval demonstrate its applicability already for a small number of laboratories.

In applications using a linear regression model with a balanced two-fold nested error structure, interest focuses on inferences concerning variability of the effects associated with the levels of nesting. This article proposes confidence intervals on the variance components associated with the primary and secondary levels in the model. In order to construct the confidence intervals we use a modified large sample method, generalized inference method, and Satterthwaite approximation. Computer simulation is performed to compare the proposed confidence intervals. A numerical example is provided to demonstrate the intervals.

Two-sided confidence intervals for a probability $$p$$ under a prescribed confidence level $$\gamma $$ are an elementary tool of statistical data analysis. A confidence interval has two basic quality characteristics: i) exactness, i. e., whether the actual coverage probability equals or exceeds the prescribed level $$\gamma $$ ; ii) inferential precision, measured by the length of the confidence interval. The interval provided by Clopper and Pearson (Biometrika 26:404–413, 1934) is the only exact interval actually used in statistical data analysis. Various authors have suggested shorter, i. e., more precise exact intervals. The present paper makes two contributions. i) We provide a general design scheme for minimum volume confidence regions under prior knowledge on the target parameter. ii) We apply the scheme to the problem of confidence intervals for a probability $$p$$ where prior knowledge is expressed in a flexible way by a beta distribution on a subset of the unit interval.

Null hypothesis significance tests and their p-values currently dominate the statistical evaluation of classifiers in machine learning. Here, we discuss fundamental problems of this research practice. We focus on the problem of comparing multiple fully specified classifiers on a small-sample test set. On the basis of the method by Quesenberry and Hurst, we derive confidence intervals for the effect size, i.e. the difference in true classification performance. These confidence intervals disentangle the effect size from its uncertainty and thereby provide information beyond the p-value. This additional information can drastically change the way in which classification results are currently interpreted, published and acted upon. We illustrate how our reasoning can change, depending on whether we focus on p-values or confidence intervals. We argue that the conclusions from comparative classification studies should be based primarily on effect size estimation with confidence intervals, and not on significance ...

Standard nonparametric prediction intervals for a single future observation are obtained by taking the interval between two pre-specified order statistics from the initial sample. In this paper, we consider the alternate approach of taking the shortest interval that contains a pre-specified number of the subintervals between the order statistics of the initial sample. We develop a method for determining exact confidence coefficients for such intervals, and we show that these data-driven prediction intervals outperform standard equal-tailed nonparametric prediction intervals. Specifically, they are much shorter than the standard intervals when the underlying distribution is skewed, and they are only slightly longer when the underlying distribution is symmetric. We also obtain the asymptotic approximation that to achieve exact confidence coefficient 1 − α when using the new data-driven prediction intervals with initial sample size n, approximately n ( 1 − α ) + 1.12 n α of the subintervals between the order statistics of the initial sample must be included.

We compare the sample size requirements for significance tests and confidence intervals by calculating power of each. The power of confidence interval is defined as the probability of obtaining a s...

Approximate confidence intervals are given for the lognormal regression problem. The error in the nominal level can be reduced to O(n −2), where n is the sample size. An alternative procedure is given which avoids the non-robust assumption of lognormality. This amounts to finding a confidence interval based on M-estimates for a general smooth function of both ϕ and F, where ϕ are the parameters of the general (possibly nonlinear) regression problem and F is the unknown distribution function of the residuals. The derived intervals are compared using theory, simulation and real data sets.

The construction of adequate confidence intervals for adaptive two-stage designs remains an area of ongoing research. We propose a conditional likelihood-based approach to construct a Wald confidence interval and two confidence intervals based on inverting the likelihood ratio test, one of them using first-order inference methods and the second one using higher order inference methods. The coverage probabilities of these confidence intervals, and also the average bias and mean square error of the corresponding point estimates, compare favorably with other available techniques. A small simulation study is used to evaluate the performance of the new methods. We investigate other extensions of practical interest for normal endpoints and illustrate them using real data, including the selection of more than one treatment for the second stage, selection rules based on both efficacy and safety endpoints, and the inclusion of a control/placebo arm. The new method also allows adjustment for covariates, and has been extended to deal with binomial data and other distributions from the exponential family. Although conceptually simple, the new methods have a much wider scope than the methods currently available.

Prevalence is one of the few estimates that rarely are reported with an appropriate measure of error in the parasitological literature. A minimum sample size recommendation of 15 samples, based on the relationship between sample size and standard error, likely has led to a false degree of confidence because of the nonlinear relationship between standard error and “true” 95% confidence intervals (as determined by Monte Carlo simulation or integration of the Bayesian posterior). Given that 95% confidence intervals for proportions are influenced by both sample size and the actual estimate of the proportion, there is no “gold standard” sample size beyond which estimates of binomial proportions can be considered “reliable.” This necessitates the reporting of confidence interval estimates that have been shown to be conservative, such as the Clopper-Pearson estimate, or robust, such as the Wilson score approximation, or the computationally intensive integration of the Bayesian posterior.

In this work, the exact finite-sample distribution of the median absolute deviation about the median (MAD) of continuous random variables is derived. The main results are used for providing exact confidence intervals for the scale parameter of a location–scale model, which are robust to the presence of outliers.

This paper presents a new random weighting method for confidence interval estimation for the sample -quantile. A theory is established to extend ordinary random weighting estimation from a non-smoothed function to a smoothed function, such as a kernel function. Based on this theory, a confidence interval is derived using the concept of backward critical points. The resultant confidence interval has the same length as that derived by ordinary random weighting estimation, but is distribution-free, and thus it is much more suitable for practical applications. Simulation results demonstrate that the proposed random weighting method has higher accuracy than the Bootstrap method for confidence interval estimation.

Error estimation accuracy is the salient issue regarding the validity of a classifier model. When samples are small, training-data-based error estimates tend to suffer from inaccuracy and quantification of error estimation accuracy is difficult. Numerous methods have been proposed for estimating confidence intervals for the true error based on the estimated error. This paper surveys proposed methods and quantifies their performance. Monte Carlo methods are used to obtain accurate estimates of the true confidence intervals and compare these to the intervals estimated from samples. We consider different error estimators and several proposed confidence-bound estimators. Both synthetic and real genomic data are employed. Our simulations show the majority of the confidence intervals methods have poor performance because of the difference of shape between true and estimated intervals. According to our results, the best estimation strategy is to use the 10-time 10-fold cross-validation with a confidence interval based on the standard deviation.

This chapter discusses the process of constructing confidence limits in particle physics and the reason why they can become invalid for an analysis such as the one presented in this thesis.

WOS: 000400186200049, The Behrens-Fisher problem concerns the inferences for the difference between means of two independent normal populations without the assumption of equality of variances. In this article, we compare three approximate confidence intervals and a generalized confidence interval for the Behrens-Fisher problem. We also show how to obtain simultaneous confidence intervals for the three population case (analysis of variance, ANOVA) by the Bonferroni correction factor. We conduct an extensive simulation study to evaluate these methods in respect to their type I error rate, power, expected confidence interval width, and coverage probability. Finally, the considered methods are applied to two real dataset., Research Foundation of Anadolu University [1202F38], This study is supported by the Research Foundation of Anadolu University (Project Number: 1202F38).

Semi-functional partial linear regression model allows to deal with a nonparametric and a linear component within the functional regression. Naive and wild bootstrap procedures are proposed to approximate the distribution of the estimators for each component in the model, and their asymptotic validities are obtained in the context of dependence data, under α-mixing conditions. Based on that bootstrap procedures, confidence intervals can be obtained for each component in the model, which can be also extended to deal with prediction intervals and prediction densities.

In its orthodoxy standard frequentist statistics deals only with aleatory probability, suppressing the intuitive epistemic probability representing inferential uncertainty. Confidence distributions, which are posterior distributions not based on any Bayesian priors, are discussed in nontechnical terms, with emphasis on the confidence curve. The correspondence between confidence curves and likelihoods allows independent confidence curves and confidence intervals to be integrated. Confidence and (serious) p -values are interpreted as epistemic probabilities, which do not fully follow ordinary probability calculus. Dimension reduction and other operations might be done on the likelihood related to the confidence curve. Confidence distributions and objective Bayes have much in common.

Statistical Model Checking (SMC) is an approximate verification method that overcomes the state space explosion problem for probabilistic systems by Monte Carlo simulations. Simulations might be however costly if many samples are required. It is thus necessary to implement efficient algorithms to reduce the sample size while preserving precision and accuracy. In the literature, some sequential schemes have been provided for the estimation of property occurrence based on predefined confidence and absolute or relative error. Nevertheless, these algorithms remain conservative and may result in huge sample sizes if the required precision standards are demanding. In this article, we compare some useful bounds and some sequential methods based on frequentist estimations. We propose outperforming and rigorous alternative schemes, based on Massart bounds and robust confidence intervals. Our theoretical and empirical analysis show that our proposal reduces the sample size while providing guarantees on error bounds.

Longitudinal investigations, where subjects are followed over time, have played an increasingly prominent role in medicine, health, and psychology in the last decades. This chapter will address inference for a two-level mixed model for a longitudinal study where observational units are clustered at both levels. Bootstrap confidence intervals for model parameters are investigated under the issues of non-normality and limited sample size of the original data. A one stage case-resampling bootstrap will be established for constructing confidence intervals by sampling clusters with replacement at the higher level. A two-stage case-resampling bootstrap will be developed by sampling clusters with replacement at the higher level and then sampling with replacement at the lower level also. Monte-Carlo simulations will be utilized to evaluate the effectiveness of these bootstrap methods with various size clusters for the mixed-effects model in terms of bias, standard deviation and confidence interval coverage for the fixed effects as well as for variance components of the random effects . The results show that the parametric bootstrap and cluster bootstrap at the higher level perform better than the two-stage bootstrap . The bootstrap methods will be applied to a longitudinal study of preschool children nested within classrooms.

This paper presents a simple methodology for estimating confidence intervals of quantiles in queueing systems. The paper investigates the actual probability density function of quantile estimators resulting of independent replications. Furthermore, we present a methodology, based on the concepts of bootstrapping, i.e., re-sampling and sub-sampling, to calculate the variability of an estimator without running different independent replications. Contrary to what overlapping and non-overlapping batching procedures suggest, we propose to randomly select data points to form a sub-sample, instead of selecting time-consecutive data points. The results of this study suggest that this proposal reduces the correlation between sub-samples (or batches) and overcomes the issue of normality.

We define confidence sets and intervals based on exact and approximate distribution theory. We consider also Bayesian intervals for the binomial special case.

In stratified matched-pair studies, risk difference between two proportions is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presents five simultaneous confidence intervals and two bootstrap simultaneous confidence intervals for risk differences in stratified matched-pair designs. The proposed confidence intervals are evaluated with respect to their coverage probabilities, expected widths, and ratios of the mesial noncoverage to noncoverage probability. Empirical results show that (1) hybrid simultaneous confidence intervals outperform nonhybrid simultaneous confidence intervals; (2) hybrid simultaneous confidence intervals based on median estimator outperform those based on maximum likelihood estimator; and (3) hybrid simultaneous confidence intervals incorporated with Wilson score and Agresti coull intervals and the bootstrap t-percentile simultaneous interval based on median unbiased estimators behave satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the prespecified nominal confidence level, and their ratios of the mesial noncoverage to noncoverage probabilities lie in [0.4,0.6] and are hence recommended. Real examples from clinical studies are used to illustrate the proposed methodologies.

The construction of a set of simultaneous confidence intervals for any finite number of contrasts of p generally correlated normal means is considered. It is shown that the simultaneous confidence level can be expressed as a ( p - 2 ) -dimensional integral for a general p ? 3 . This expression allows one to compute quickly and accurately, by using numerical quadrature, the required critical constants and multiplicity adjusted p -values for at least p = 3 , 4 and 5, involving only one-, two- and three-dimensional integrals, respectively. Real data examples from a drug stability study and a dose response study are used to illustrate the method.

Extreme value estimation, such as maximum wave height estimation, is critical for robust and cost efficient design of ocean structure. Some previous methods are incapable of quantifying the confidence interval when taking variance of shape parameter into account. The authors propose a new method based on likelihood. The utilization of group likelihood, profile likelihood and deviation method permits the use of likelihood inference for extreme value estimation, even when the distribution is non-regular. The authors conducted a Monte Carlo experiment to show the performance of this new method for 3 parameter Weibull distribution. The authors also revealed the problems with Goda's estimation method. The robust results suggest the use of likelihood inference to quantify the statistical uncertainty and the asymmetric distribution of confidence intervals, which have been overlooked in previous studies.

In this study, we proposed to use the nonparametric bootstrap procedure to construct the confidence interval for the mean correlation r corrected for Case IV range restriction in meta-analysis (i.e., ; Hunter, Schmidt, & Le, 2006). A comprehensive Monte Carlo study was conducted to evaluate the accuracy of the parametric confidence interval and 3 nonparametric bootstrap confidence intervals for r(c4). Of the 4 intervals, our results showed that the bootstrap bias-corrected and accelerated percentile interval (BCaI) yielded the most accurate results across different data situations. In addition, the mean-corrected correlation r(c4) was found to be more accurate than the uncorrected estimate. Implications of the mean-corrected correlation r(c4) and BCaI in organizational studies are also discussed.

This paper presents the new confidence interval for the coefficient of variation of lognormal distribution with restricted parameter. We proved the coverage probability and expected length of our proposed confidence interval.

In simple static linear simultaneous equation models the empirical distributions ofIV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. It is demonstrated why in this context the limiting distribution of a consistent estimator is not a¤ected by conditioning on exogenous regressors, whereas that of an inconsistent estimator is. The asymptotic variance and the simulated actual variance of the inconsistent OLS estimator are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of consistent IV estimation and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background the consequences for the identification of the parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressors and disturbances. This leads to a feasible procedure for constructing purely OLS-based robust confidence intervals, which yield conservative coverage probabilities in finite samples, and often outperform IV-based intervals regarding their length.

Now we extend one method into a sequence of binomial data, propose a stepwise confidence interval method for toxic-ity study, and also in our paper, two methods of constructing intervals for the risk difference are proposed. The first one is based on the well-known conditional confidence intervals for odds ratio, and the other one comes from Santner“small-sample confidence intervals for the difference of two success probabilities”, and it produces exact intervals, through employing our method.

Using two measurements, we produce an estimate of the mean and the sample standard deviation. We construct a confidence interval with these parameters and compute the probability of the confidence interval by using the cumulative distribution function and averaging over the parameters. The probability is in the form of an integral that we compare to a computer simulation.

Principal component analysis (PCA) is widely used as a tool in (exploratory) data investigations for many different research areas such as analytical chemistry, food- and pharmaceutical-research, and multivariate statistical process control. Despite its popularity, not many results have been reported thus far on how to calculate reliable confidence interval limits in PCA estimates. And, like all other data analysis tasks, results of PCA are not complete without reasonable expectations for the parameter uncertainties, especially in the case of predictive model objectives. In this paper we will present a case study on how to calculate confidence limits based on bootstrap re-sampling. Two NIR datasets are used to build bootstrap confidence limits. The first dataset shows the effect of outliers on bootstrap confidence limits, while the second shows the bootstrap confidence limits when the data has a bimodal distribution. The different steps and choices which have to be made for the algorithm to perform correctly will be presented. The bootstrap based confidence limits will be compared with the corresponding asymptotic confidence limits. We will thereby conclude that the confidence limits based on the bootstrap method give more meaningful answers and are to be preferred over its asymptotic counterparts.

One of challenging problems for indoor wireless multi-floor positioning systems is a presence of Reference Node (RN) failures, which causes the missing of the values of Received Signal Strength (RSS) during the online positioning phase of the fingerprinting technique. This leads to performance degradation in terms of floor accuracy which affects other localization procedures. This paper presents a robust floor determination algorithm called Robust Confidence Interval Sum-RSS (RCIS), which can accurately determine the floor where mobile objects located and can work under either the fault-free scenario or the RN-failure scenarios. The proposed fault tolerance floor algorithm is based on the confidence interval of the summation of the strongest RSS obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSNs) during the online phase. The performance of the proposed algorithm is compared with those of different floor determination algorithms in literature. The experimental results show that the proposed robust floor determination algorithm outperformed the other floor algorithms and can achieve the highest percentage of floor determination accuracy in all tested scenarios. Specifically, the proposed algorithm can achieve 100% correct floor determination under the scenario in which 40% of RNs failed.

Traditional process capability indices require that quality characteristics follow normal distribution. But in the actual production processes, quality characteristic usually has a non-normal distribution and almost all the production processes exhibit the between batch variability besides the within batch variability. This paper proposed confidence intervals for process capability indices for log-normal process under the one-way random model based on the generalized confidence interval. Motivated by the generalized confidence intervals, the confidence interval of the process capability indices of log-normal distribution are constructed based on the one-way random model. The good performance of generalized lower confidence limits and its coverage probabilities are studied via simulation, and simulation results show the good performance of the generalized confidence interval method in the log-normal distribution case. Finally, examples are provided to illustrate the implementation of the proposed method.

Background Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative. Methods We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained. Results Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest. Conclusions We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the ‘1–4 % split’, where greater tail probability is allocated to the upper confidence bound. The ‘width-optimal’ interval that we present deserves further investigation. Electronic supplementary material The online version of this article (doi:10.1186/s12874-016-0219-y) contains supplementary material, which is available to authorized users.

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes

The Hartley-Rao-Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley-Rao-Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re-sampling, linearization, variance estimation, design-effects or joint inclusion probabilities.

In the last decade, it has been shown that an adaptive testing method could be used, along with the Robbins–Monro search procedure, to obtain confidence intervals that are often narrower than traditional confidence intervals. However, these confidence interval limits require a great deal of computation and some familiarity with stochastic search methods. We propose a method for estimating the limits of confidence intervals that uses only a few tests of significance. We compare these limits to those obtained by a lengthy Robbins–Monro stochastic search and find that the proposed method is nearly as accurate as the Robbins–Monro search. Adaptive confidence intervals that are produced by the proposed method are often narrower than traditional confidence intervals when the distributions are long-tailed, skewed, or bimodal. Moreover, the proposed method of estimating confidence interval limits is easy to understand, because it is based solely on the p-values from a few tests of significance.

This paper describes the application of high-confidence-interval prediction methods to the aircraft trajectory prediction problem, more specifically to the altitude prediction during climb. We are interested in methods for finding two-sided intervals that contain, with a specified confidence, at least a desired proportion of the conditional distribution of the response variable. This paper introduces two-sided Bonferroni-quantile confidence intervals, which is a new method for obtaining high-confidence two-sided intervals in quantile regression. This paper also uses the Bonferroni inequality to propose a new method for obtaining tolerance intervals in least squares regression. The latter has the advantages of being reliable, fast, and easy to calculate. We compare physical point-mass models to the introduced models on an air traffic management data set composed of traffic at major French airports. Experimental results show that the proposed interval prediction models perform significantly better than the conventional point-mass model currently used in most trajectory predictors. When comparing with a recent state-of-the-art point-mass model with adaptive mass estimation, the proposed methods give altitude intervals that are slightly wider but more reliable.

In this paper, interval estimation for the Birnbaum-Saunders distribution is considered. The generalized confidence intervals for the shape parameter and some important reliability quantities such as its mean, quantiles and reliability function are explored. A simulation study illustrates the accuracy of these generalized confidence intervals. Finally, two numerical examples are used to illustrate the proposed procedures.

The problem of robust estimation and multivariate outlier detection of the term structure of default intensity is considered. Both the multivariate Vasicek and CIR models, embedding the Kalman filter algorithm in a forward search context, are used to estimate default intensity. The focus is not on the estimation of credit models including jumps, but on the automatic detection of masked multiple outliers in multivariate time series. Both simulated and real market credit spread time series are analyzed. In order to make inference on outliers, confidence envelopes which are virtually independent of the estimated parameters are introduced. The output is not only a unique default intensity term structure curve, as often used in the financial literature, but a robust confidence interval within which default intensity is likely to stay.

In this article, we investigated the bootstrap calibrated generalized confidence limits for process capability indices C pk for the one-way random effect model. Also, we derived Bissell's approximation formula for the lower confidence limit using Satterthwaite's method and calculated its coverage probabilities and expected values. Then we compared it with standard bootstrap (SB) method and generalized confidence interval method. The simulation results indicate that the confidence limit obtained offers satisfactory coverage probabilities. The proposed method is illustrated with the help of simulation studies and data sets.

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter θ is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given level of significance in many cases; and, therefore, the corresponding intervals are no longer confidence intervals in terms of the actual definition. In the present work, confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing. Two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach.