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Sequential (or adaptive) designs are common in acceptance sampling and pharmaceutical trials. This is because they can achieve the same type 1 and type 2 error rate with fewer subjects on average than fixed sample trials. After the trial is completed and the test result decided, we need full inference on the main parameter Δ. In this paper, we are interested in exact one-sided lower and upper limits. Unlike standard trials, for sequential trials there need not be an explicit test statistic, nor even p -value. This motivates the more general approach of defining an ordering on the sample space and using the construction of Buehler (1957). This is guaranteed to produce exact limits, however, there is no guarantee that the limits will agree with the test. For instance, we might reject Δ ≤ Δ 0 at level α but have a lower 1 − α limit being less then Δ 0. This paper gives a very simple condition to ensure that this unfortunate feature does not occur. When the condition fails, the ordering is easily modified to ensure compatibility. • For sequential tests, it is unclear how to define a p-value which can be inverted to a confidence limit. • Consequently, confidence limits can conflict with the results of a sequential test. • For discrete endpoints, standard approximate limits have poor accuracy so we seek exact limits. • Exact limits also need not agree with the results of an exact sequential test. • We give a simple easily checked condition that ensures agreement. [ABSTRACT FROM AUTHOR]

We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) in misspecified mixed model analysis. Previous studies have shown that, in spite of the model misspecification, certain quantities of genetic interests are consistently estimable, and consistent estimators of these quantities can be obtained using the restricted maximum likelihood (REML) method under a misspecified linear mixed model. However, the asymptotic variance of such a REML estimator is complicated and not ready to be implemented for practical use. In this paper, we develop practical and computationally convenient methods for estimating such asymptotic variances and constructing the associated confidence intervals. Performance of the proposed methods is evaluated empirically based on Monte-Carlo simulations and real-data application. • We propose variance estimators for restricted maximum likelihood estimators of heritiability and variance components in genome-wide association studies under misspecified mixed model analysis. • We also present associated confidence intervals. • Our proposed method and the genome-based restricted maximum likelihood (GREML) method under genome-wide complex trait analysis have similar performance in simulation studies and data application, which may provide justification for GREML. [ABSTRACT FROM AUTHOR]

Abstract The Gini correlation plays an important role in measuring dependence of random variables with heavy tailed distributions, whose properties are a mixture of Pearson's and Spearman's correlations. Due to the structure of this dependence measure, there are two Gini correlations between each pair of random variables, which are not equal in general. Both the Gini correlation and the equality of the two Gini correlations play important roles in Economics. In the literature, there are limited papers focusing on the inference of the Gini correlations and their equality testing. In this paper, we develop the jackknife empirical likelihood (JEL) approach for the single Gini correlation, for testing the equality of the two Gini correlations, and for the Gini correlations' differences of two independent samples. The standard limiting chi-square distributions of those jackknife empirical likelihood ratio statistics are established and used to construct confidence intervals, rejection regions, and to calculate p -values of the tests. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals, as well as in terms of power of the tests. The proposed methods are illustrated in an application on a real data set from UCI Machine Learning Repository. Highlights • JEL's for Gini correlations have limiting Chi-square distributions. • JEL approach for Gini correlations enjoys a computational advantage. • JEL approach is effective in terms of short confidence interval and high power. [ABSTRACT FROM AUTHOR]

In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) methods are proposed to construct a nonparametric confidence interval for the mean difference of two independent zero-inflated skewed populations. The JEL and AJEL confidence intervals are compared with the confidence intervals by normal approximation and empirical likelihood proposed by Zhou and Zhou (2005). Simulation studies are performed to assess the new methods. Two real-life datasets are also used as an illustration of the proposed methodologies. • The jackknife empirical likelihood is proposed for the mean difference of two zero-inflated skewed populations. • The adjusted jackknife empirical likelihood confidence interval is developed for the mean difference. • The proposed confidence intervals are compared with the existing ones. • Simulation studies are performed to assess the new methods. • Two data sets are used as an illustration of the proposed interval estimates. [ABSTRACT FROM AUTHOR]

This paper considers screening of adaptive interventions or adaptive treatment strategies embedded in a sequential multiple assignment randomized trial (SMART). As a SMART typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. We propose simultaneous confidence intervals that compare the values of interventions of interest to that of the unknown best intervention by generalizing the method in Edwards and Hsu (1983). The multiple comparison with the best (MCB) intervals are applied as screening tool: an intervention with MCB interval excluding zero will be declared as inferior to the true best at a pre-specified confidence level, and hence excluded from further exploration. Simulation studies show that the proposed method outperforms the multiple comparison procedures based on Bonferroni's correction in terms of width of confidence intervals for estimation. The method is applied to analyze data from the CODIACS trial in patients with depression. • A sequential multiple assignment randomized trial (SMART) typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. • We propose simultaneous confidence intervals that compare the values of interventions of interest to that of the unknown best intervention by generalizing the method in Edwards and Hsu (1983). • The multiple comparison with the best (MCB) intervals are applied as screening tool: An intervention with MCB interval excluding zero will be declared as inferior to the true best at a pre-specified confidence level, and hence excluded from further exploration. • Simulation studies show that the proposed method outperforms the multiple comparison procedures based on Bonferroni's correction in terms of width of confidence intervals for estimation. • The method is applied to analyze data from the CODIACS trial in patients with depression. [ABSTRACT FROM AUTHOR]

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is useful because it gives a stable estimate for a mean of a small area. For measuring uncertainty of EBLUP, much of research is focused on second-order unbiased estimation of mean squared prediction errors in the univariate case. In this paper, we consider the multivariate Fay–Herriot model where the covariance matrix of random effects is fully unknown, and obtain a confidence region of the small area mean that is based on the Mahalanobis distance centered around EBLUP and has second-order correction. A positive-definite, consistent and second-order unbiased estimator of the covariance matrix of the random effects is also suggested. The performance is investigated through simulation study. • We construct a confidence region based on the Mahalanobis distance centered around EBLUP with second-order accuracy. • This confidence region can be written in closed form and has little burden in computation. • We suggest a new method for obtaining a positive-definite and second-order unbiased estimator of the covariance matrix of random effects. [ABSTRACT FROM AUTHOR]

Often a problem in linear regression either for correlated data or high-dimensional data is the singularity of the sample covariance matrix. While dealing with an ill-conditioned covariance matrix has been a longstanding challenge in the statistical literature, recent proposals relying on adding noises to the original data have found their successes in obtaining reliable estimates and making predictions. It has been shown that perturbing data with noises has a close relationship to the well-known ridge estimator. In this paper, we propose to add noises to the predictors with a known covariance structure, and call the estimator obtained in such a way a "pseudo estimator". A new variable selection procedure based on the concept of pseudo confidence interval which works for both correlated predictors and "large p small n " problem is proposed. We study the theoretical properties of the proposed pseudo estimator and variable selection procedure. Furthermore, we use an ensemble step to stabilize the pseudo estimation (variable selection) results. The advantages of the proposed method are demonstrated by both simulation studies and real data analyses. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops statistical inference for population quantiles based on a partially rank-ordered set (PROS) sample design. A PROS sample design is similar to a ranked set sample with some clear differences. This design first creates partially rank-ordered subsets by allowing ties whenever the units in a set cannot be ranked with high confidence. It then selects a unit for full measurement at random from one of these partially rank-ordered subsets. The paper develops a point estimator, confidence interval and hypothesis testing procedure for the population quantile of order p. Exact, as well as asymptotic, distribution of the test statistic is derived. It is shown that the null distribution of the test statistic is distribution-free, and statistical inference is reasonably robust against possible ranking errors in ranking process. [Copyright &y& Elsevier]

Abstract: It is widely accepted that jumps exist in the asset price process. The jump activity index is a natural measure of how frequent the jumps are. Statistical inference of the jump activity index is of importance in determining the type of process that underlies the dynamics of the log price process. In this paper, we implement the empirical likelihood approach to construct the confidence interval of the jump activity index of a pure jump model using high frequency data. Wilks'' theorem is established. We also extend the result on ''s estimator to the more general framework in this paper. Simulation studies demonstrate the good performance of the empirical likelihood approach. Compared with the existing non-parametric estimator proposed by , the empirical likelihood approach gives more accurate coverage probabilities in the simulation studies. [Copyright &y& Elsevier]

Abstract: The lognormal distribution is currently used extensively to describe the distribution of positive random variables. This is especially the case with data pertaining to occupational health and other biological data. One particular application of the data is statistical inference with regards to the mean of the data. Other authors, namely , have proposed procedures involving the so-called “method of variance estimates recovery” (MOVER), while an alternative approach based on simulation is the so-called generalized confidence interval, discussed by . In this paper we compare the performance of the MOVER-based confidence interval estimates and the generalized confidence interval procedure to coverage of credibility intervals obtained using Bayesian methodology using a variety of different prior distributions to estimate the appropriateness of each. An extensive simulation study is conducted to evaluate the coverage accuracy and interval width of the proposed methods. For the Bayesian approach both the equal-tail and highest posterior density (HPD) credibility intervals are presented. Various prior distributions (Independence Jeffreys'' prior, Jeffreys''-Rule prior, namely, the square root of the determinant of the Fisher Information matrix, reference and probability-matching priors) are evaluated and compared to determine which give the best coverage with the most efficient interval width. The simulation studies show that the constructed Bayesian confidence intervals have satisfying coverage probabilities and in some cases outperform the MOVER and generalized confidence interval results. The Bayesian inference procedures (hypothesis tests and confidence intervals) are also extended to the difference between two lognormal means as well as to the case of zero-valued observations and confidence intervals for the lognormal variance. In the last section of this paper the bivariate lognormal distribution is discussed and Bayesian confidence intervals are obtained for the difference between two correlated lognormal means as well as for the ratio of lognormal variances, using nine different priors. [Copyright &y& Elsevier]

Abstract: In recent years, the Quintile Share Ratio (or QSR) has become a very popular measure of inequality. In 2001, the European Council decided that income inequality in European Union member states should be described using two indicators: the Gini Index and the QSR. The QSR is generally defined as the ratio of the total income earned by the richest 20% of the population relative to that earned by the poorest 20%. Thus, it can be expressed using quantile shares, where a quantile share is the share of total income earned by all of the units up to a given quantile. The aim of this paper is to propose an improved methodology for the estimation and variance estimation of the QSR in a complex sampling design framework. Because the QSR is a non-linear function of interest, the estimation of its sampling variance requires advanced methodology. Moreover, a non-trivial obstacle in the estimation of quantile shares in finite populations is the non-unique definition of a quantile. Thus, two different conceptions of the quantile share are presented in the paper, leading us to two different estimators of the QSR. Regarding variance estimation, proposed a variance estimator based on linearization techniques. However, his method involves Gaussian kernel smoothing of cumulative distribution functions. Our approach, also based on linearization, shows that no smoothing is needed. The construction of confidence intervals is discussed and a proposition is made to account for the skewness of the sampling distribution of the QSR. Finally, simulation studies are run to assess the relevance of our theoretical results. [Copyright &y& Elsevier]

Abstract: The methodology for deriving the exact confidence coefficient of some confidence intervals for a binomial proportion is proposed in Wang [2007. Exact confidence coefficients of confidence intervals for a binomial proportion. Statist. Sinica 17, 361–368]. The methodology requires two conditions of confidence intervals: the monotone boundary property and the full coverage property. In this paper, we show that for some confidence intervals of a binomial proportion, the two properties hold for any sample size. Based on results presented in this paper, the procedure in Wang [2007. Exact confidence coefficients of confidence intervals for a binomial proportion. Statist. Sinica 17, 361–368] can be directly used to calculate the exact confidence coefficients of these confidence intervals for any fixed sample size. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the proposal of optimality criteria, referred to as X- and -optimality criteria, and the construction of X- and -optimal designs, for nonlinear regression models. These optimal designs aim at improving the estimation of parameters of this class of models. The principle of these criteria is the minimization, with respect to the design, of the expected volume of a particular exact parametric confidence region. In this paper we give detailed definitions, properties, and computation methods of X- and -optimal designs. We also compare these designs with the classic local D-optimal designs, with regard to robustness and efficiency, for two very well-known academic models (Box–Lucas and Michaelis–Menten models). [Copyright &y& Elsevier]

Abstract: In many statistical problems, the variances of the populations cannot be assumed to be equal. These inhomogeneity problems are often more difficult to handle than the corresponding homogeneity problems. In sequential estimation, this often means that only first order sequential procedures are available in the statistics literature for inhomogeneity problems. The purpose of this paper is to illustrate by using the classical Behrens–Fisher problem how to construct a second order sequential procedure using the batch sampling idea of Hall [Ann. Statist. 9 (1981) 1229–1238]; the cost of assuming variance inhomogeneity even when the two variances are equal turns out to be very limited. The approach of this paper can readily be applied to many other inhomogeneous problems. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of simultaneously estimating multiple ratios. In the simplest case of only one ratio parameter, Fieller''s theorem (J. Roy. Statist. Soc. Ser. B 16 (1954) 175) provides a confidence interval for the single ratio. For multiple ratios, there is no method available to construct simultaneous confidence intervals that exactly satisfy a given familywise confidence level. Many of the methods in use are conservative since they are based on probability inequalities. In this paper, first we consider exact simultaneous confidence sets based on the multivariate t-distribution. Two approaches of determining the exact simultaneous confidence sets are outlined. Second, approximate simultaneous confidence intervals based on the multivariate t-distribution with estimated correlation matrix and a resampling approach are discussed. The methods are applied to ratios of linear combinations of the means in the one-way layout and ratios of parameter combinations in the general linear model. Extensive Monte Carlo simulation is carried out to compare the performance of the various methods with respect to the stability of the estimated critical points and of the coverage probabilities. [Copyright &y& Elsevier]

In order to construct prediction intervals without the cumbersome–and typically unjustifiable–assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studied in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the construction of bootstrap prediction intervals. Forward and backward bootstrap methods using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as estimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their achieved coverage level and length of interval. [ABSTRACT FROM AUTHOR]

We consider a functional linear regression model with scalar response and functional covariate. For this model bootstrap confidence intervals for prediction using the residual resampling method have been already studied. In this paper, we use the paired resampling method to construct bootstrap confidence intervals for prediction in the functional linear regression model. We develop Edgeworth expansions for distribution of the prediction and apply the results to obtain coverage errors of percentile equal-tailed bootstrap confidence intervals for prediction. We carry out a simulation study to illustrate the numerical performance of the paired bootstrap confidence intervals and compare the results with those obtained by the residual resampling method. [ABSTRACT FROM AUTHOR]

Abstract: Interval estimation of the area under the receiver operating characteristic (ROC) curve is difficult when working with right-censored data. An empirical likelihood method is not advisable in this case due to severe computational issues. In this paper we propose an extension of a so-called weighted empirical likelihood (WEL) method for interval estimation of this parameter. We define the WEL ratio and show that it has a limiting scaled chi-square distribution. This result allows us to construct a confidence interval for the area under the ROC curve. Finally we conduct a simulation study to compare the performance of the proposed WEL-based interval with the one based on already existing plug-in method. [Copyright &y& Elsevier]

Abstract: In this paper, using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two independent samples and construct the confidence intervals. We prove that the limiting distribution of the empirical log-likelihood ratio is a chi-squared distribution like Shen and He (2007). In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation methods with the optimal bandwidth selected by cross-validation. The empirical likelihood method has a better performance most of the time. Finally, a real clinical trial data is used to illustrate how to generate empirical likelihood confidence bands using bootstrap method. [Copyright &y& Elsevier]

Abstract: If the power spectral density of a continuous time stationary stochastic process is not limited to a finite bandwidth, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum estimators, which are unsuitable for constructing confidence intervals. In this paper, we use the smoothed periodogram estimator to construct asymptotic confidence intervals shrinking to the true spectra, by allowing the sampling rate to go to infinity suitably fast as the sample size goes to infinity. The proposed method requires minimal computation, as it does not involve bootstrap or other resampling. The method is illustrated through a Monte-Carlo simulation study, and its performance is compared with that of the corresponding method based on uniform sampling at a fixed rate. [Copyright &y& Elsevier]

Abstract: This paper considers 2×2 tables arising from case–control studies in which the binary exposure may be misclassified. We found circumstances under which the inverse matrix method provides a more efficient odds ratio estimator than the naive estimator. We provide some intuition for the findings, and also provide a formula for obtaining the minimum size of a validation study such that the variance of the odds ratio estimator from the inverse matrix method is smaller than that of the naive estimator, thereby ensuring an advantage for the misclassification corrected result. As a corollary of this result, we show that correcting for misclassification does not necessarily lead to a widening of the confidence intervals, but, rather, in addition to producing a consistent estimate, can also produce one that is more efficient. [Copyright &y& Elsevier]

Abstract: This paper focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model-based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its strength from easy access to a good-fitting model among a plethora of choices available for binary response data. The substantive methodological contribution is in exploiting a semiparametric estimator of the survival function to produce improved simultaneous confidence bands. To obtain critical values for computing the confidence bands, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carried out to check efficacy. The method is illustrated using two lung cancer data sets. [Copyright &y& Elsevier]

Abstract: We use bias-reduced estimators of high quantiles of heavy-tailed distributions, to introduce a new estimator for the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked in a simulation study, by four of the most popular goodness-of-fit tests. The accuracy of the resulting confidence intervals is evaluated as well. We also investigate the finite sample behavior and compare our estimator with some versions of Peng''s estimator of the mean (namely those based on Hill, t-Hill and Huisman et al. extreme value index estimators). Moreover, we discuss the robustness of the tail index estimators used in this paper. Finally, our estimation procedure is applied to the well-known Danish fire insurance claims data set, to provide confidence bounds for the means of weekly and monthly maximum losses over a period of 10 years. [Copyright &y& Elsevier]

Abstract: The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performance of two or more laboratory or diagnostic tests. In this paper, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric and the other one is non-parametric and both have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It is shown that the log-semi-empirical likelihood ratio statistic is asymptotically scaled chi-squared. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. We conduct extensive simulation studies to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing probabilities. [Copyright &y& Elsevier]

Abstract: We are concerned with the problem of estimating the treatment effects at the effective doses in a dose-finding study. Under monotone dose–response, the effective doses can be identified through the estimation of the minimum effective dose, for which there is an extensive set of statistical tools. In particular, when a fixed-sequence multiple testing procedure is used to estimate the minimum effective dose, show that the confidence lower bounds for the treatment effects can be constructed without the need to adjust for multiplicity. Their method, called the dose–response method, is simple to use, but does not account for the magnitude of the observed treatment effects. As a result, the dose–response method will estimate the treatment effects at effective doses with confidence bounds invariably identical to the hypothesized value. In this paper, we propose an error-splitting method as a variant of the dose–response method to construct confidence bounds at the identified effective doses after a fixed-sequence multiple testing procedure. Our proposed method has the virtue of simplicity as in the dose–response method, preserves the nominal coverage probability, and provides sharper bounds than the dose–response method in most cases. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a multivariate linear model with complete/incomplete data, where the regression coefficients are subject to a set of linear inequality restrictions. We first develop an expectation/conditional maximization (ECM) algorithm for calculating restricted maximum likelihood estimates of parameters of interest. We then establish the corresponding convergence properties for the proposed ECM algorithm. Applications to growth curve models and linear mixed models are presented. Confidence interval construction via the double-bootstrap method is provided. Some simulation studies are performed and a real example is used to illustrate the proposed methods. [Copyright &y& Elsevier]

Abstract: The paper considers the construction of a confidence band for the trend function of a stationary time series. An explicit formula is derived based on polynomial splines and . The performance of the confidence band is illustrated by simulation studies. The proposed method is applied to the analysis of the annual yields of wheat in the United States. [Copyright &y& Elsevier]

Abstract: The transformation model plays an important role in survival analysis. In this paper, we investigate the linear transformation model based on new empirical likelihood. Motivated by and , we introduce the truncated survival time and adjust each term of estimating equations to improve the accuracy of coverage probability. We prove that the log-likelihood ratio has the asymptotic distribution . The new empirical likelihood method avoids estimating the complicated covariance matrix in contrast to normal approximation method and empirical likelihood method developed by . Moreover, the proposed method enables us to obtain confidence intervals for the component of regression parameters. In the simulation study, our method demonstrates better performance than the traditional method in the small samples. [Copyright &y& Elsevier]

Abstract: In this paper, we study the construction of confidence intervals for a probability density function under a (positively) associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ2-type distributed. The result is used to obtain EL-based confidence interval for the probability density function. [Copyright &y& Elsevier]

Abstract: We develop in this paper a new procedure to construct simultaneous confidence bands for derivatives of mean curves in functional data analysis. The technique involves polynomial splines that provide an approximation to the derivatives of the mean functions, the covariance functions and the associated eigenfunctions. We show that the proposed procedure has desirable statistical properties. In particular, we first show that the proposed estimators of derivatives of the mean curves are semiparametrically efficient. Second, we establish consistency results for derivatives of covariance functions and their eigenfunctions. Most importantly, we show that the proposed spline confidence bands are asymptotically efficient as if all random trajectories were observed with no error. Finally, the confidence band procedure is illustrated through numerical simulation studies and a real life example. [Copyright &y& Elsevier]

Abstract: In this paper, we consider to apply the empirical likelihood method to a probability density function under an associated sample. It is shown that the empirical likelihood ratio statistic is asymptotically distributed under some mild conditions. The result is used to construct empirical likelihood-based confidence intervals on the probability density function. [Copyright &y& Elsevier]

Abstract: The tolerance interval receives very much attention in literature and is widely applied in industry. However, it is generally constructed through the criterion of minimum width by . Although effort for clarification of several prediction related intervals has been made recently by , the appropriateness of the tolerance interval for its role in industry applications is insufficiently discussed. According to manufacturers'' requests, a concept of admissibility of tolerance intervals is defined in this paper and we show that these types of tolerance intervals are not admissible due to short of confidence. We further prove that a confidence interval of a interval is admissible and is appropriate for use. [Copyright &y& Elsevier]

Abstract: Constructing a confidence interval for a binomial proportion is one of the most basic problems in statistics. The score interval as well as the Wilson interval with some modified forms have been broadly investigated and suggested by many statisticians. In this paper, a generalized score interval CI G(a) is proposed by replacing the coefficient 1/4 in the score interval with parameter a. Based on analyzing and comparing various confidence intervals, we recommend the generalized score interval CI G(0.3) for the nominal confidence levels 0.90, 0.95 and 0.99, which improves the spike phenomenon of the score interval and behaves better and computes more easily than most of other approximate intervals such as the Agresti–Coull interval and the Jeffreys interval to estimate a binomial proportion. [Copyright &y& Elsevier]

Abstract: This paper deals with the interval estimation of when X and Y are two independent generalized Pareto random variables with a common scale parameters. An asymptotic confidence interval for is constructed based on the modified signed log-likelihood ratio statistic. Monte Carlo simulations are performed to illustrate the accuracy of the proposed method. [Copyright &y& Elsevier]

Abstract: In scenarios where the variance of a response variable can be attributed to two sources of variation, a confidence interval for a ratio of variance components gives information about the relative importance of the two sources. For example, if measurements taken from different laboratories are nine times more variable than the measurements taken from within the laboratories, then 90% of the variance in the responses is due to the variability amongst the laboratories and 10% of the variance in the responses is due to the variability within the laboratories. Assuming normally distributed sources of variation, confidence intervals for variance components are readily available. In this paper, however, simulation studies are conducted to evaluate the performance of confidence intervals under non-normal distribution assumptions. Confidence intervals based on the pivotal quantity method, fiducial inference, and the large-sample properties of the restricted maximum likelihood (REML) estimator are considered. Simulation results and an empirical example suggest that the REML-based confidence interval is favored over the other two procedures in unbalanced one-way random effects model. [Copyright &y& Elsevier]

Abstract: Variable selection in regression analysis is of importance because it can simplify model and enhance predictability. After variable selection, however, the resulting working model may be biased when it does not contain all of significant variables. As a result, the commonly used parameter estimation is either inconsistent or needs estimating high-dimensional nuisance parameter with very strong assumptions for consistency, and the corresponding confidence region is invalid when the bias is relatively large. We in this paper introduce a simulation-based procedure to reformulate a new model so as to reduce the bias of the working model, with no need to estimate high-dimensional nuisance parameter. The resulting estimators of the parameters in the working model are asymptotic normally distributed whether the bias is small or large. Furthermore, together with the empirical likelihood, we build simulation-based confidence regions for the parameters in the working model. The newly proposed estimators and confidence regions outperform existing ones in the sense of consistency. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of fixed-width confidence interval estimation of the location of a negative exponential distribution with unknown scale . Suppose we have information on the scale parameter such that where is known to the experimenter from past experiences. We propose a two-stage procedure and provide higher order asymptotic expansions of the expected sample size and the coverage probability. [Copyright &y& Elsevier]

Abstract: Let X 1,…,X n be some i.i.d. observations from a heavy-tailed distribution F, i.e. the common distribution of the excesses over a high threshold u n can be approximated by a generalized Pareto distribution with . This paper deals with the problem of finding confidence regions for the couple : combining the empirical likelihood methodology with estimation equations (close but not identical to the likelihood equations) introduced by , asymptotically valid confidence regions for are obtained and proved to perform better than Wald-type confidence regions (especially those derived from the asymptotic normality of the maximum likelihood estimators). By profiling out the scale parameter, confidence intervals for the tail index are also derived. [Copyright &y& Elsevier]

Abstract: The paper uses the empirical likelihood method to study the construction of confidence intervals and regions for regression coefficients and response mean in generalized linear models with missing response. By using the inverse selection probability weighted imputation technique, the proposed empirical likelihood ratios are asymptotically chi-squared. Our approach is to directly calibrate the empirical likelihood ratio, which is called as a bias-correction method. Also, a class of estimators for the parameters of interest is constructed, and the asymptotic distributions of the proposed estimators are obtained. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths/areas of confidence intervals/regions. An example of a real data set is used for illustrating our methods. [Copyright &y& Elsevier]

Abstract: Consider the nonparametric heteroscedastic regression model , where is an unknown conditional mean function and is an unknown conditional scale function. In this paper, the limit distribution of the quantile estimate for the scale function is derived. Since the limit distribution depends on the unknown density of the errors, an empirical likelihood ratio statistic based on quantile estimator is proposed. This statistics is used to construct confidence intervals for the variance function. Under certain regularity conditions, it is shown that the quantile estimate of the scale function converges to a Brownian motion and the empirical likelihood ratio statistic converges to a chi-squared random variable. Simulation results demonstrate the superiority of the proposed method over the least squares procedure when the underlying errors have heavy tails. [Copyright &y& Elsevier]

Abstract: In this paper, we study the construction of confidence intervals for quantiles of a population under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically distributed. The result is used to obtain EL based confidence intervals for quantiles of a population. Results of a simulation study on the finite sample performance of the proposed confidence intervals are reported. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the construction of confidence intervals for a probability density function under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically distributed. The result is used to obtain EL based confidence interval on the probability density function. [ABSTRACT FROM AUTHOR]

Abstract: We have considered the functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameter is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. In this paper, we have proposed an alternative approach in order to obtain pointwise confidence intervals by means of a bootstrap procedure, for which we have obtained its asymptotic validity. Besides, a simulation study allows us to compare the practical behaviour of asymptotic and bootstrap confidence intervals in terms of coverage rates for different sample sizes. [ABSTRACT FROM AUTHOR]

Abstract: This paper is motivated by the pioneering work of Emanuel Parzen wherein he advanced the estimation of (spectral) densities via kernel smoothing and established the role of reproducing kernel Hilbert spaces (RKHS) in field of time series analysis. Here, we consider analysis of power (ANOPOW) for replicated time series collected in an experimental design where the main goals are to estimate, and to detect differences among, group spectra. To accomplish these goals, we obtain smooth estimators of the group spectra by assuming that each spectral density is in some RKHS; we then apply penalized least squares in a smoothing spline ANOPOW. For inference, we obtain simultaneous confidence intervals for the estimated group spectra via bootstrapping. [ABSTRACT FROM AUTHOR]

Abstract: Suppose that we have a linear regression model with random error , where X is a random design variable and is observed completely, and Y is the response variable and some Y-values are missing at random (MAR). In this paper, based on the ‘complete’ data set for Y after inverse probability weighted imputation, we construct empirical likelihood statistics on EY and which have the -type limiting distributions under some new conditions compared with Xue (2009). Our results broaden the applicable scope of the approach combined with . [Copyright &y& Elsevier]

Abstract: In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates, in form of confidence intervals on the parameters of interest. The length of a confidence interval characterizes the accuracy of the whole findings. Consequently, confidence intervals should be constructed to hold a desired length. Basic ideas go back to and who proposed a two-stage procedure for hypothesis testing about a normal mean. additionally considered the probability or power a confidence interval should possess to hold its length within a desired boundary. In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein''s concept. Concrete rules for sample size updating are provided. Following an adaptive two-stage design of type, a real data example is worked out in detail. [Copyright &y& Elsevier]

Abstract: The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting non-exponential, heavy-tailed distributions of interarrival times and different scaling properties. We establish the asymptotic normality of our estimators for the two parameters appearing in our fPp model. This fact permits construction of the corresponding confidence intervals. The properties of the estimators are then tested using simulated data. [Copyright &y& Elsevier]

Abstract: This paper considers the one-sample sign test for population quantiles in general ranked set sampling, and proposes a weighted sign test because observations with different ranks are not identically distributed. It is shown analytically that optimal weight always improves the Pitman efficiency for all distributions. For each quantile, the sampling allocation that maximizes the sign test efficacy is identified and shown to not depend on the population distribution. Moreover, distribution-free confidence intervals for quantiles based on ordered values of optimal ranked set samples are discussed. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a two-stage sampling method () for making inferences on the means of two normal populations with heteroscedastic variances which is usually referred to as the Behrens–Fisher problem (). The two-stage method can be used to control Type-II error and the length of confidence interval conditional on a specified Type-I error or confidence level. Simulation results show that the two-stage method improves the powers of the tests and its performance exhibits superior robustness properties over the existing single-stage methods. Moreover, our method can be easily extended to compare multiple populations. [Copyright &y& Elsevier]

Abstract: A simultaneous confidence band provides useful information on the plausible range of an unknown regression model. For simple linear regression models, the most frequently quoted bands in the statistical literature include the hyperbolic band and the three-segment bands. One interesting question is whether one can construct confidence bands better than the hyperbolic and three-segment bands. The optimality criteria for confidence bands include the average width criterion considered by and among others, and the minimum area confidence set (MACS) criterion of . In this paper, two families of exact confidence bands, the inner-hyperbolic bands and the outer-hyperbolic bands, which include the hyperbolic and three-segment bands as special cases, are introduced in simple linear regression. Under the MACS criterion, the best confidence band within each family is found by numerical search and compared with the hyperbolic band, the best three-segment band and with each other. The methodologies are illustrated with a numerical example and the Matlab programs used are available upon request. [Copyright &y& Elsevier]