In medical diagnostic studies, the area under the receiver operating characteristic curve (AUC) is a widely used metric that captures a continuous test's overall ability to discriminate between diseased and non-diseased individuals across all possible cutoffs. However, in practice, disease status is sometimes only partially verified, introducing verification bias that undermines the validity of AUC estimation. While numerous methods address bias correction for AUC estimation, approaches that directly construct confidence intervals for the AUC remain limited. This paper proposes two robust methods for constructing bias-corrected confidence intervals for the AUC under the missing-at-random assumption: one based on bootstrap resampling and the other on empirical likelihood. Both approaches accommodate missing disease verification by leveraging the bias-corrected ROC estimators introduced by Alonzo and Pepe. Extensive simulation studies and real-world data analyses demonstrate that our proposed methods yield valid and precise interval estimates for the AUC under various clinically relevant settings.

In this article, we address the statistical inference problem proposed for the sparse spatio-temporal autoregressive models with additive measurement error when the number of spatial nodes exceeds the number of temporal observations. We use the improved Yule-Walker estimation method, adding the bagging algorithm to the estimation process to solve the over-identification problem. The simulation-extrapolation (SIMEX) method is used to reduce the influence of additive measurement error and we confirm the feasibility of empirical likelihood method to establish confidence intervals for model coefficients. Furthermore, some simulations and real examples are carried out to evaluate the finite sample performance.

This paper focuses on the application of the Bayesian jackknife empirical likelihood method to survey data collected from general single-stage unequal probability sampling and stratified sampling designs. We examine parameters characterized by U-statistics and establish the regularity conditions under which the posterior distribution, derived from the Bayesian jackknife pseudo-empirical likelihood under different priors, converges asymptotically to a normal distribution. We also investigate the impact of incorporating auxiliary information, as well as the use of design weights and calibration weights. Through simulations and real data analysis, we evaluate the effectiveness of the Bayesian jackknife pseudo-empirical likelihood credible intervals. Our results demonstrate that the proposed methodology not only offers significant advantages over methods that ignore the sampling design but also outperforms jackknife pseudo-empirical likelihood approaches.

Heavy-tailed distributions, such as the Cauchy distribution, are acknowledged for providing more accurate models for financial returns, as the normal distribution is deemed insufficient for capturing the significant fluctuations observed in real-world assets. In this paper, we develop goodness-of-fit tests for the standard Cauchy distribution based on the characterization. The asymptotic distribution of the test statistic is obtained. Additionally, we proposed a jackknife empirical likelihood (JEL)-based test. Extensive Monte Carlo simulation studies are conducted to evaluate the finite sample performance of the proposed tests. The simulation results show that the proposed tests have good power compared to others. Finally, the applicability of the novel tests is demonstrated with several real-data examples.

We propose a novel jackknife pseudo-empirical likelihood approach for analyzing survey data from general unequal probability sampling designs. This method is applicable to finite population parameters defined by U-statistics. Theoretical results show that the jackknife pseudo-empirical likelihood ratio statistic asymptotically follows a chi-squared distribution. We further consider scenarios with or without auxiliary information, incorporating either design weights or calibration weights. Through numerical studies, we evaluate the performance of the jackknife pseudo-empirical likelihood ratio confidence intervals in terms of coverage probabilities and tail error rates. Our findings demonstrate that the proposed method outperforms those based on the normal approximation.

This paper considers pointwise inference for nonparametric estimating equations models. The paper proposes two general test statistics that are based on a local version of the Generalised Empirical Likelihood (GEL) approach that can be used to test simple hypotheses about the unknown infinite dimensional parameters and to test for the correct specification of the chosen nonparametric estimating equations model. The paper shows that among the class of the proposed GEL test statistics, the empirical likelihood ratio is the only one admitting a Bartlett correction, however by appropriately modifying the other GEL based test statistics, it is still possible to obtain second order accurate inferences. The paper also proposes a new (local) version of the so-called efficient bootstrap that delivers the same level of second order accuracy as that of the (modified) GEL test statistics for the correct specification of the chosen nonparametric estimating equations model. Finally, the paper uses simulations and a real data example to illustrate the finite sample properties and applicability of the proposed inference methods.

Testing for serial correlation is fundamental in regression analysis, yet methods for matrix-type data remain limited. This paper develops a test for serial correlation within the trace regression framework. By extending empirical likelihood to matrix data, we propose an empirical log-likelihood ratio statistic. Its asymptotic distribution is derived under both the null and local alternatives. Some simulations are conducted to demonstrate its finite-sample performance. Finally, the proposed test is applied to straw-burning fire-point data, confirming its practical utility.

In the paper, we study the estimation and empirical likelihood of the parameter of interest in semiparametric varying coefficient models with right censored response data. The doubly robust and efficient estimation, along with bias-corrected empirical likelihood ratio of the regression parameter are constructed, and the estimators of the coefficient functions and the link function are also constructed. The uniformly convergence rates and asymptotic normality of the proposed estimators are presented, and the consistent estimators of the asymptotic variances are given. A more efficient estimation of the regression parameter is obtained, and the Wilks' phenomenon of the proposed ratio is proved. The obtained results can be directly used to construct confidence regions/intervals for the regression parameter and pointwise confidence intervals for the coefficient functions. The proposed method is evaluated by a simulation study and illustrated by real data analysis.

Empirical likelihood test for the mean with inequality constraints under strong mixing high-frequency data

While empirical likelihood methods offer the advantages of being distribution-free and data-adaptive, their conventional implementations deteriorate significantly under high-dimensional moment constraints. This limitation poses substantial challenges for practical applications in spatial autoregressive models with autoregressive disturbances (SARSAR models). To overcome this limitation, we propose a principal component empirical likelihood (PCEL) methodology for tackling high-dimensional moment constraints in the spatial model. This approach innovatively transforms high-dimensional constraints on the scoring function into low-dimensional constraints while maximizing information retention. Theoretical analysis demonstrates that the PCEL ratio statistics asymptotically follow chi-squared distributions, enabling the construction of confidence regions for high-dimensional parameters in SARSAR models. Simulation results demonstrate that the PCEL method achieves coverage probabilities significantly closer to nominal confidence levels compared to both usual EL and modified EL approaches. Furthermore, PCEL maintains robust performance even in ultra-high-dimensional regimes where EL fails. Finally, we conduct an empirical analysis on a classical spatial dataset.

This paper focuses on estimating the multivariate coefficient of variation for an unobservable variable vector plagued by multiplicative distortion measurement errors, where the observable variable is a multiplicative blend of the unobservable vector and an unknown contaminating function linked to a confounding variable. By employing conditional mean and absolute mean calibration techniques, we derive a calibrated vector and introduce the calibrated Van Valen’s multivariate coefficient of variation. We rigorously establish the asymptotic properties of estimators to lay a solid theoretical foundation. To enhance inference precision, we construct confidence intervals using both asymptotic normality and empirical likelihood methods, ensuring flexibility and robustness. Additionally, we propose test statistics to check if each component of the unobservable vector follows a “curved” normal distribution, vital for uncovering underlying distributional traits. Through extensive simulations and real-world data analysis from the Regensburg Pediatric Appendicitis dataset, we validate the robustness and effectiveness of our approach, demonstrating its broad applicability in scenarios involving unobservable variables with multiplicative distortion errors.

ABSTRACT Quantiles are used to measure risk or return in risk management and investment decision-making, while the data available in finance are often of high-frequency. In this paper, we study the joint confidence regions for a finite number of quantiles under strong mixing high-frequency data by employing the blockwise empirical likelihood (EL) method and the blockwise adjust empirical likelihood (AEL) method. We firstly construct the blockwise EL ratio statistic and the blockwise AEL ratio statistic for a finite number of quantiles and prove their asymptotic properties. Then we conduct simulations which show that the confidence regions based on the AEL method perform better than the EL method and the normal approximation method. As an application of our theoretic results, we also give an empirical analysis for real data.

To study whether air pollution is detrimental to reproductive development is imperative. In the absence of randomized trials to study the effects of air pollution on human health, data from observational studies have been utilized in which the researchers attempted to capture the causal associations between air pollution and the health outcomes. Many of these studies rely on parametric assumptions which may be limiting. In this tutorial, we explain and implement the nonparametric Empirical Likelihood (EL) Algorithm within the causal inference framework of a classic methodology and a newer technique based on machine learning tools. We show the competitive results of the assumption free EL in simulations. We also apply the developed methods to study the causal association between PM2.5 and NO2 exposure and anogenital distance at birth, a marker of androgen activity.

ABSTRACT This paper introduces new robust methods for multiple-sample statistical inference based on L-estimators. We present revised versions of the two-sample t-test and the ANOVA F-test, and develop empirical likelihood tests for comparing the differences between two L-estimators as well as among k independent sample L-estimators. The simulation study presented in this paper shows that the proposed methods produce similar results to those of classical approaches when data is generated from a normal distribution. However, when contaminated normal distributions were considered, the proposed methods offered clear advantages.

Linear and nonlinear variable selection by a non-penalized approach in ultra-high dimensions

Jackknife empirical likelihood ratio test for independence between a continuous and a categorical random variable

This paper proposes a new covariance-based measure to evaluate the symmetry of continuous random variables, focusing on covariance between the square root of density and distribution functions, suitable for uniform distributions. It applies the measure to test exponential distribution adherence and, in undistorted scenarios, introduces two nonparametric exponential parameter estimators, one achieving asymptotic efficiency akin to maximum likelihood estimators. The paper derives asymptotic properties of the measure, uses empirical likelihood for inference, and extends analysis to a multiplicative distortion model with an unknown smoothing function. Through conditional mean calibration, calibrated variables are obtained, and estimators for exponential parameters and the measure are constructed, maintaining asymptotic efficiency for the estimated measure. Empirical likelihood confidence intervals and tests for exponentiality under distortion are developed. Monte Carlo simulations and a real dataset validate the proposed estimators and test statistics.

In fields such as industry and finance, large amounts of data with heterogeneous characteristics are often generated. Traditional statistical models struggle to address the modeling problems associated with such data. The joint mean and variance model provides a new approach to handle these data. Since its introduction, various challenges related to the model, such as parameter estimation, variable selection, empirical likelihood inference, and statistical diagnostics, have been extensively studied. However, in practical applications, many heterogeneous datasets undergo structural changes at certain points due to various factors. Ignoring such changes during data analysis might lead to errors in the results, and more severely, it may affect decision-making, causing significant losses. To address this issue, this paper focuses on the joint mean and variance model under a normal distribution and proposes a change point test method based on the Modified Information Criterion (MIC) to tackle the change point problem in heteroscedastic data. Simulation results reveal that the MIC-based test method significantly outperforms the classical likelihood ratio test. Finally, the method is applied to the analysis of the China Securities 2000 Index return dataset, successfully identifying the location of the change points within the data.

Empirical likelihood for partially linear functional-coefficient autoregressive errors-in-variables models

Abstract Nonresponse in probability sampling presents a long‐standing challenge in survey sampling, often necessitating simultaneous adjustments to address sampling and selection biases. We develop a statistical framework that explicitly models sampling weights as random variables and establish the semiparametric efficiency bound for the parameter of interest under nonresponse. This study investigates strategies for eliminating bias and effectively utilizing available information, extending beyond nonresponse issues to data integration with external summary statistics. The proposed estimators are characterized by their efficiency and double robustness. However, realizing full efficiency hinges on the accurate specification of underlying models. To enhance robustness against potential model misspecification, we expand double robustness to multiple robustness through a novel two‐step empirical likelihood approach. A numerical study evaluates the finite‐sample performance of our methods. Additionally, we apply these methods to a dataset from the National Health and Nutrition Examination Survey, effectively integrating summary statistics from the National Health Interview Survey.