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This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis. [ABSTRACT FROM AUTHOR]

Through exploiting information from the source data to improve the fit performance on the target data, transfer learning estimations for high‐dimensional linear regression models have drawn much attention recently, but few studies focus on statistical inference and robust learning in the presence of heavy‐tailed/asymmetric errors. Using adaptive Huber regression (AHR) to achieve the bias and robustness tradeoff, in this paper we propose a robust transfer learning algorithm with high‐dimensional covariates, then construct valid confidence intervals and hypothesis tests based on the debiased lasso approach. When the transferable sources are known, a two‐step ℓ1$$ {\ell}_1 $$‐penalized transfer AHR estimator is firstly proposed and the error bounds are established. To correct the biases caused by the lasso penalty, a unified debiasing framework based on the decorrelated score equations is considered to establish asymptotic normality of the debiased lasso transfer AHR estimator. Confidence intervals and hypothesis tests for each component can be constructed. When the transferable sources are unknown, a data‐driven source detection algorithm is proposed with theoretical guarantee. Numerical studies verify the performance of our proposed estimator and confidence intervals, and an application to Genotype‐Tissue Expression data is also presented. [ABSTRACT FROM AUTHOR]

Well‐recommended methods of forming "confidence intervals" for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal confidence level. The methods are favoured because their intervals have a shorter average length than the Clopper–Pearson (gold‐standard) method, whose intervals really are confidence intervals. As the definition of a confidence interval is not being adhered to, another criterion for forming interval estimates for a binomial proportion is needed. In this paper, we suggest a new criterion for forming one‐sided intervals and equal‐tail two‐sided intervals. Methods which meet the criterion are said to yield locally correct confidence intervals. We propose a method that yields such intervals and prove that its intervals have a shorter average length than those of any other method that meets the criterion. Compared with the Clopper–Pearson method, the proposed method gives intervals with an appreciably smaller average length. For confidence levels of practical interest, the mid‐p method also satisfies the new criterion and has its own optimality property. It gives locally correct confidence intervals that are only slightly wider than those of the new method. [ABSTRACT FROM AUTHOR]

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy‐tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second‐order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto‐type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle‐point approximation, from which a second set of new confidence intervals follows. The small‐sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance. [ABSTRACT FROM AUTHOR]

Wilks's theorem is useful for constructing confidence regions. When applying the popular empirical likelihood to data with nonignorable nonresponses, Wilks's phenomenon does not hold. This paper unveils that this is caused by the extra estimation of the nuisance parameter in the nonignorable nonresponse propensity. Motivated by this result, we propose an adjusted empirical likelihood for which Wilks's theorem holds. Asymptotic results are presented and supplemented by simulation results for finite sample performance of the point estimators and confidence regions. An analysis of a data set is included for illustration. [ABSTRACT FROM AUTHOR]

Abstract: The starting point in uncertainty quantification is a stochastic model, which is fitted to a technical system in a suitable way, and prediction of uncertainty is carried out within this stochastic model. In any application, such a model will not be perfect, so any uncertainty quantification from such a model has to take into account the inadequacy of the model. In this paper, we rigorously show how the observed data of the technical system can be used to build a conservative non‐asymptotic confidence interval on quantiles related to experiments with the technical system. The construction of this confidence interval is based on concentration inequalities and order statistics. An asymptotic bound on the length of this confidence interval is presented. Here we assume that engineers use more and more of their knowledge to build models with order of errors bounded by l o g ( n ) / n. The results are illustrated by applying the newly proposed approach to real and simulated data. [ABSTRACT FROM AUTHOR]

Estimation of time-average variance constant (TAVC), which is the asymptotic variance of the sample mean of a dependent process, is of fundamental importance in various fields of statistics. For frequentists, it is crucial for constructing confidence interval of mean and serving as a normalizing constant in various test statistics and so forth. For Bayesians, it is widely used for evaluating effective sample size and conducting convergence diagnosis in Markov chain Monte Carlo method. In this paper, by considering high-order corrections to the asymptotic biases, we develop a new class of TAVC estimators that enjoys optimal [ABSTRACT FROM AUTHOR]

This paper proposes the use of the integrated likelihood for inference on the mean effect in small-sample meta-analysis for continuous outcomes. The method eliminates the nuisance parameters given by variance components through integration with respect to a suitable weight function, with no need to estimate them. The integrated likelihood approach takes into proper account the estimation uncertainty of within-study variances, thus providing confidence intervals with empirical coverage closer to nominal levels than standard likelihood methods. The improvement is remarkable when either (i) the number of studies is small to moderate or (ii) the small sample size of the studies does not allow to consider the within-study variances as known, as common in applications. Moreover, the use of the integrated likelihood avoids numerical pitfalls related to the estimation of variance components which can affect alternative likelihood approaches. The proposed methodology is illustrated via simulation and applied to a meta-analysis study in nutritional science. [ABSTRACT FROM AUTHOR]

Recently, a technique based on pseudo-observations has been proposed to tackle the so-called convex hull problem for the empirical likelihood statistic. The resulting adjusted empirical likelihood also achieves the high-order precision of the Bartlett correction. Nevertheless, the technique induces an upper bound on the resulting statistic that may lead, in certain circumstances, to worthless confidence regions equal to the whole parameter space. In this paper, we show that suitable pseudo-observations can be deployed to make each element of the generalized power divergence family Bartlett-correctable and released from the convex hull problem. Our approach is conceived to achieve this goal by means of two distinct sets of pseudo-observations with different tasks. An important effect of our formulation is to provide a solution that permits to overcome the problem of the upper bound. The proposal, which effectiveness is confirmed by simulation results, gives back attractiveness to a broad class of statistics that potentially contains good alternatives to the empirical likelihood. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study the problem of estimating the quantile function of a finite population. Attention is first focused on point estimation, and asymptotic results are obtained. Confidence intervals are then constructed, based on both the following: (i) asymptotic results and (ii) a resampling technique based on rescaling the 'usual' bootstrap. A simulation study to compare asymptotic and resampling-based results, as well as an application to a real population, is finally performed. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we derive an exact formula for the covariance of two innovations computed from a spatial Gibbs point process and suggest a fast method for estimating this covariance. We show how this methodology can be used to estimate the asymptotic covariance matrix of the maximum pseudo-likelihood estimator of the parameters of a spatial Gibbs point process model. This allows us to construct asymptotic confidence intervals for the parameters. We illustrate the efficiency of our procedure in a simulation study for several classical parametric models. The procedure is implemented in the statistical software R, and it is included in spatstat, which is an R package for analyzing spatial point patterns. [ABSTRACT FROM AUTHOR]

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

The two-stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right-censored survival data from a two-stage design. A non-parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite-sample bias of the Kaplan–Meier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study. [ABSTRACT FROM AUTHOR]

Abstract Calculation of a confidence interval for intraclass correlation to assess inter-rater reliability is problematic when the number of raters is small and the rater effect is not negligible. Intervals produced by existing methods are uninformative: the lower bound is often close to zero, even in cases where the reliability is good and the sample size is large. In this paper, we show that this problem is unavoidable without extra assumptions and we propose two new approaches. The first approach assumes that the raters are sufficiently trained and is related to a sensitivity analysis. The second approach is based on a model with fixed rater effect. Using either approach, we obtain conservative and informative confidence intervals even from samples with only two raters. We illustrate our point with data on the development of neuromotor functions in children and adolescents. [ABSTRACT FROM AUTHOR]

In traditional bootstrap applications the size of a bootstrap sample equals the parent sample size, n say. Recent studies have shown that using a bootstrap sample size different from n may sometimes provide a more satisfactory solution. In this paper we apply the latter approach to correct for coverage error in construction of bootstrap confidence bounds. We show that the coverage error of a bootstrap percentile method confidence bound, which is of order O ( n [sup -2/2] ) typically, can be reduced to O ( n [sup -1] ) by use of an optimal bootstrap sample size. A simulation study is conducted to illustrate our findings, which also suggest that the new method yields intervals of shorter length and greater stability compared to competitors of similar coverage accuracy. [ABSTRACT FROM AUTHOR]