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We define confidence to be epistemic if it applies to an observed confidence interval. Epistemic confidence is unavailable—or even denied—in orthodox frequentist inference, as the confidence level is understood to apply to the procedure. Yet there are obvious practical and psychological needs to think about the uncertainty in the observed interval. We extend the Dutch Book argument used in the classical Bayesian justification of subjective probability to a stronger market‐based version, which prevents external agents from exploiting unused information in any relevant subset. We previously showed that confidence is an extended likelihood, and the likelihood principle states that the likelihood contains all the information in the data, hence leaving no relevant subset. Intuitively, this implies that confidence associated with the full likelihood is protected from the Dutch Book, and hence is epistemic. Our goal is to validate this intuitive notion through theoretical backing and practical illustrations. [ABSTRACT FROM AUTHOR]

When we study any queuing system, the performance measures reflect different features of the system. In the classical M/M/1 queuing system, traffic intensity is perhaps the most important performance measure. We propose a fresh and simple estimator for the same and show that it has nice properties. Our approach is frequentist. This approach has the dual advantage of practical usability and familiarity. Our proposed estimator is attractive as it possesses desirable properties. We have shown how our estimator lends itself to testing of hypothesis. Confidence intervals are constructed. Sample size determination is also discussed. A comparison with a few similar estimators is also performed. [ABSTRACT FROM AUTHOR]

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is an important problem and Taylor linearization method is often used to reflect the effect of estimating the propensity score weights. In this article, we propose an approximate Bayesian approach to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is calibrated to the frequentist inference in that the credible region obtained from the posterior distribution asymptotically matches to the frequentist confidence interval obtained from the Taylor linearization method. The proposed Bayesian method is also extended to incorporate the auxiliary information from full sample. Results from limited simulation studies confirm the validity of the proposed methods. The proposed method is applied to data from a Korean longitudinal survey. [ABSTRACT FROM AUTHOR]

The use of real-world data became more and more popular in the pharmaceutical industry. The impact of real-world evidence is now well emphasized by the regulatory authorities. Indeed, the analysis of this type of data can play a key role for treatment efficacy and safety. The aim of this work is to assess various methods and give guidance on the comparisons of drugs, mostly with respect to time-to-event data, in non-randomized studies with potentially confounding variables. For that purpose, several statistical methodologies are compared based on simulation studies. These methodologies belong to family classes of methods that are widely used for this type of problem: regression, matching, weighting and subclassification methods. The evaluation criteria used to compare methods performances are the relative bias, the mean square error, the coverage probability and the width of the confidence interval. In this paper, we consider different scenarios of dataset features in order to study the effect of the sample size, the number of covariates and the magnitude of the treatment effect on the statistical methodologies performances. These statistical analyses are conducted within a proportional hazard model framework. Furthermore, we highlight the advantage of using techniques to identify relevant covariates for time-to-event outcomes by comparing two variable selection methods under a frequentist and a Bayesian inference. Based on simulation results, recommendations on each of the family of methods are provided to guide decision making. [ABSTRACT FROM AUTHOR]

Our main contribution is to examine the reliability of confidence intervals using the SAM state-space fish stock assessment model used for the assessment of many stocks by the International Council for the Exploration of the Seas. We focus on frequentist statistical inferences and more specifically on inference conditioned on specific values of the state-space model random effects drawn from their process distribution. This is somewhat consistent with simulation self-test procedures that are commonly used to examine the reliability of state-space assessment model results. However, recent research has indicated that some estimation bias may be expected in the conditional setting. Hence, we also investigate recently proposed bias corrected confidence intervals appropriate for the conditional inference setting. The SAM simulation coverage probabilities of 95% confidence intervals for SSB and Fbar were usually slightly larger than 95%, but in a small number of years these coverage probabilities could be much smaller than 95%. The bias corrected confidence intervals were more reliable. When averaged over years, the SAM and bias corrected confidence interval coverage probabilities were similar for the Northeast Artic cod and saithe case studies, but the bias corrected confidence intervals performed much better overall for the haddock case study. [ABSTRACT FROM AUTHOR]

Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator's variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size. [ABSTRACT FROM AUTHOR]

Multiple imputation has become one of the most popular approaches for handling missing data in statistical analyses. Part of this success is due to Rubin's simple combination rules. These give frequentist valid inferences when the imputation and analysis procedures are so-called congenial and the embedding model is correctly specified, but otherwise may not. Roughly speaking, congeniality corresponds to whether the imputation and analysis models make different assumptions about the data. In practice, imputation models and analysis procedures are often not congenial, such that tests may not have the correct size, and confidence interval coverage deviates from the advertised level. We examine a number of recent proposals which combine bootstrapping with multiple imputation and determine which are valid under uncongeniality and model misspecification. Imputation followed by bootstrapping generally does not result in valid variance estimates under uncongeniality or misspecification, whereas certain bootstrap followed by imputation methods do. We recommend a particular computationally efficient variant of bootstrapping followed by imputation. [ABSTRACT FROM AUTHOR]

Background: Various methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test. However, traditional methods are known to suffer from truncation of the prevalence estimate and the confidence intervals constructed around the point estimate, as well as from under-performance of the confidence intervals' coverage.Methods: In this study, we used simulated data sets to validate a Bayesian prevalence estimation method and compare its performance to frequentist methods, i.e. the Rogan-Gladen estimate for prevalence, RGE, in combination with several methods of confidence interval construction. Our performance measures are (i) error distribution of the point estimate against the simulated true prevalence and (ii) coverage and length of the confidence interval, or credible interval in the case of the Bayesian method.Results: Across all data sets, the Bayesian point estimate and the RGE produced similar error distributions with slight advantages of the former over the latter. In addition, the Bayesian estimate did not suffer from the RGE's truncation problem at zero or unity. With respect to coverage performance of the confidence and credible intervals, all of the traditional frequentist methods exhibited strong under-coverage, whereas the Bayesian credible interval as well as a newly developed frequentist method by Lang and Reiczigel performed as desired, with the Bayesian method having a very slight advantage in terms of interval length.Conclusion: The Bayesian prevalence estimation method should be prefered over traditional frequentist methods. An acceptable alternative is to combine the Rogan-Gladen point estimate with the Lang-Reiczigel confidence interval. [ABSTRACT FROM AUTHOR]

Ecological data often violate common assumptions of traditional parametric statistics (e.g., that residuals are Normally distributed, have constant variance, and cases are independent). Modern statistical methods are well equipped to handle these complications, but they can be challenging for non-statisticians to understand and implement. Rather than default to increasingly complex statistical methods, resampling-based methods can sometimes provide an alternative method for performing statistical inference, while also facilitating a deeper understanding of foundational concepts in frequentist statistics (e.g., sampling distributions, confidence intervals, p-values). Using simple examples and case studies, we demonstrate how resampling-based methods can help elucidate core statistical concepts and provide alternative methods for tackling challenging problems across a broad range of ecological applications. [ABSTRACT FROM AUTHOR]

When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-informative. In spite of this, we argue that the uniform prior is not suitable as a default prior for inference about a regression coefficient in the context of the bio-medical and social sciences. We propose that a more suitable default choice is the normal distribution with mean zero and standard deviation equal to the standard error of the M-estimator. We base this recommendation on two arguments. First, we show that this prior is non-informative for inference about the sign of the regression coefficient. Second, we show that this prior agrees well with a meta-analysis of 50 articles from the MEDLINE database. [ABSTRACT FROM AUTHOR]

Abstract: Frequentist model averaging has been proposed as a method for incorporating “model uncertainty” into confidence interval construction. Such proposals have been of particular interest in the environmental and ecological statistics communities. A promising method of this type is the model averaged tail area (MATA) confidence interval put forward by Turek & Fletcher (2012). The performance of this interval depends greatly on the data‐based model weights. A computationally convenient formula for the coverage probability of this interval was provided by Kabaila, Welsh, & Abeysekera (2016), in the simple scenario of two nested linear regression models. We consider more complicated scenarios with a large number of linear regression models. For each of a given set of components of the regression parameter vector, we either set the component to zero or let it vary freely. We provide an easily computed upper bound on the minimum coverage probability of the MATA confidence interval. This upper bound provides evidence against the use of a model weight based on the Bayesian Information Criterion (BIC). The Canadian Journal of Statistics 46: 279–297; 2018 © 2018 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

We study the frequentist properties of confidence intervals found with various methods previously proposed for the On–Off problem. We derive explicit formulas for the limits and calculate the true coverage and the expected lengths of these methods. [ABSTRACT FROM AUTHOR]

We present a (selective) review of recent frequentist highdimensional inference methods for constructing p-values and confidence intervals in linear and generalized linear models. We include a broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the Rpackage h d i which easily allows the use of different methods and supports reproducibility. [ABSTRACT FROM AUTHOR]

Hydrological modelling has become an intensively studied subject in recent years. One of the most significant problems concerning this issue is to provide mathematical and statistical tools, which allow to forecast extreme hydrological events, such as severe sea or river floodings. In particular, the estimation of flood quantiles is often needed in hydrological design to construct reliable flood defences. In our paper, we establish procedures leading to the interval estimation of the quantiles of the maxima of sea levels. We mainly focus on the quantile estimation for the distributions of the 3-day maxima of sea levels, although some general patterns involving the quantile estimation for the distributions of the m-day maxima of sea levels, where m>3, are also delivered. The introduced estimation scheme uses the Peaks over Threshold (POT) approach as one of theoretical frameworks. We propose the Frequentistic and Bayesian approaches in the constructions of our confidence intervals (CIs). The choice of optimal threshold in the presented method based on the POT approach is discussed as well. The coverage probabilities for the corresponding CIs are also computed. [ABSTRACT FROM AUTHOR]

The problem of efficiently computing the orbital elements of a visual binary while still deriving confidence intervals with frequentist properties is treated. When formulated in terms of the Thiele-Innes elements, the known distribution of probability in Thiele-Innes space allows efficient grid-search plus Monte-Carlo-sampling schemes to be constructed for both the minimum-χ2 and the Bayesian approaches to parameter estimation. Numerical experiments with 104 independent realizations of an observed orbit confirm that the 1− and 2σ confidence and credibility intervals have coverage fractions close to their frequentist values. [ABSTRACT FROM AUTHOR]

An important contribution to the literature on frequentist model averaging (FMA) is the work of Hjort and Claeskens (2003), who developed an asymptotic theory for frequentist model averaging in parametric models based on a local mis-specification framework. They also proposed a simple method for constructing confidence intervals of the unknown parameters. This article shows that the confidence intervals based on the FMA estimator suggested by Hjort and Claeskens (2003) are asymptotically equivalent to that obtained from the full model under both parametric and the varying-coefficient partially linear models. Thus, as long as interval estimation rather than point estimation is concerned, the confidence interval based on the full model already fulfills the objective and model averaging provides no additional useful information. [ABSTRACT FROM AUTHOR]

Consider a linear regression model with n-dimensional response vector, regression parameter [ABSTRACT FROM AUTHOR]

The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed-two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly. [ABSTRACT FROM AUTHOR]

SUMMARY Testing and confidence interval construction for a parameter are achieved by constructing a pivotal. In this paper we study construction of approximate pivotals from recapture models where capture probabilities possibly vary from occasion to occasion. We compare the asymptotic standard normality of various pivotals including analogues of the classical maximum likelihood/Wald, score and likelihood ratio statistics. Some bias adjustments are developed and indicate that the score pivotal has smaller bias than the pivotal of Chao (1989). The score and likelihood ratio pivotals both provide intervals with accurate two-sided coverage, but one-sided coverage accuracy varies. Chao's pivotal appears to be slightly conservative but is the simplest to compute. Classical pivotals based directly on the estimator are inadequate. [ABSTRACT FROM AUTHOR]

Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higher-order matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior agrees with the prior matching the posterior and frequentist expansions based on the signed square root of log-likelihood ratio. The normal, inverse Gaussian, and gamma distributions are used to illustrate the results. [ABSTRACT FROM AUTHOR]