Jackknife Empirical Likelihood Research Articles

A new portmanteau test for predictive regression models with possible embedded endogeneity

In the widely used predictive regression model, any possible serial correlation in innovations leads to estimation bias and statistical inference distortions. Hence, it is important to pretest the existence of such serial correlation. Nevertheless, in the presence of embedded endogeneity, which is a common problem in the predictive regression setting, traditional serial correlation tests such as Box–Pierce (BP) and Ljung–Box (LB) tests are found to perform poorly. Motivated by this, we develop a new portmanteau test in this article as a pretest for serial correlation in predictive regression under possible embedded endogeneity. This test is based on the sample splitting idea and the jackknife empirical likelihood method. The asymptotic distribution of the proposed test has been derived, and the Monte Carlo simulations confirm good finite sample performances. As an illustration, we apply our proposed test in pretesting the serial correlation in predictive regression, where financial variables are used to predict the excess return of S&P 500.

Jackknife empirical likelihood for the correlation coefficient with multiplicative distortion measurement errors

In this paper, we consider the estimation problem of a correlation coefficient between two unobserved variables of interest that are distorted in a multiplicative way by some unobserved confounding variable. We investigate the direct plug-in estimator of the correlation coefficient. We propose using jackknife empirical likelihood (JEL) and its variations to construct confidence intervals for the correlation coefficient based on the estimator. The proposed JEL statistic is shown to be asymptotically a standard chi-squared distribution. We compare our methods to the previous empirical likelihood (EL) techniques of Zhang et al. (2014, ‘A Revisit to Correlation Analysis for Distortion Measurement Error Data’, Journal of Multivariate Analysis, 124, 116–129) and show the JEL possesses better small sample properties. Simulation studies are conducted to examine the performance of the proposed estimator, and we also use our proposed methods to analyse the Boston housing data for illustration.

Bayesian empirical likelihood inference for the mean absolute deviation

The mean absolute deviation (MAD) is a direct measure of the dispersion of a random variable about its mean. In this paper, the empirical likelihood (EL) and the adjusted EL methods for the MAD are proposed. The Bayesian empirical likelihood, the Bayesian adjusted empirical likelihood, the Bayesian jackknife empirical likelihood and the Bayesian adjusted jackknife empirical likelihood methods are used to construct credible intervals for the MAD. Simulation results show that the proposed EL method performs better than the JEL in Zhao et al. [Jackknife empirical likelihood inference for the mean absolute deviation. Comput Stat Data Anal. 2015;91:92–101], and the proper prior information improves coverage rates of confidence/credible intervals. Two real datasets are used to illustrate the new procedures.

Confidence intervals for heterogeneity in meta-analysis of the rare binary events based on empirical likelihood-type methods

In meta-analysis, heterogeneity between independent studies is one of the important reference indicators for comprehensive analyses. It is usually described in terms of the variance between groups of the random-effect model. The existing methods are used to construct their confidence intervals based on the assumption of the normal distribution, but in reality, this assumption is often violated, especially in rare binary events. Recently, the method of the jackknife empirical likelihood was proposed to build confidence intervals; however, it tends to perform not as good as the parametric methods when the number of studies involved is small. Therefore, we propose to use the adjusted jackknife empirical likelihood, transformed jackknife empirical likelihood, and transformed adjusted jackknife empirical likelihood to construct confidence intervals for heterogeneity of the rare binary event. We investigate the performance of the proposed methods through the simulations based on different distributions, especially for skewed distributions and the small sample sizes. Applications to real data with the proposed methods are also provided.

Jackknife empirical likelihood confidence intervals for the categorical Gini correlation

The categorical Gini correlation, ρg, was proposed by Dang et al. (2021) to measure the dependence between a categorical variable, Y, and a numerical variable, X. It has been shown that ρg has more appealing properties than current existing dependence measurements. In this paper, we develop the jackknife empirical likelihood (JEL) method for ρg. Confidence intervals for the Gini correlation are constructed without estimating the asymptotic variance. Adjusted and weighted JEL are explored to improve the performance of the standard JEL. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals. The proposed methods are illustrated in an application on two real datasets.

Jackknife empirical likelihood ratio test for logistic distribution using fixed point characterization

Tests for the goodness of fit of logistic distribution have received much attention in the literature as it is widely used in many studies related to bio-assay, population growth, etc. In this paper, we propose a method to test whether the data comes from a logistic distribution or not. We derive the asymptotic distribution of the test statistic. Also, we develop a test based on Jackknife Empirical Likelihood (JEL). The finite sample performance of the JEL ratio test is evaluated through Monte Carlo simulation. We illustrate the proposed method using a real data set.

Jackknife empirical likelihood based diagnostic checking for Ar(p) models

Jackknife empirical likelihood based diagnostic checking for Ar(p) models

Jackknife empirical likelihood for the lower-mean ratio

Measuring economic inequality is an important topic to explore the social system. The Gini index and Pietra ratio are used by many people but are limited to reflecting the sampling distribution. In this paper, we study the interval estimates with another measure called the lower mean ratio u. By using jackknife empirical likelihood (JEL), adjusted jackknife empirical likelihood (AJEL), mean jackknife empirical likelihood (MJEL), mean adjusted jackknife empirical likelihood (MAJEL), and adjusted mean jackknife empirical likelihood methods, we propose the interval estimator for u. In the simulation study, we make a comparison of these methods in terms of coverage probability and average confidence interval length. The simulation results indicate that MAJEL performs the best among these methods for small sample sizes of the skewed distribution. For a small sample size of normal distribution, both JEL and MJEL show better performance than the other methods but MJEL is relatively time-consuming. Finally, two real data sets are analysed to illustrate the proposed methods.

General Jackknife empirical likelihood and its applications

General Jackknife empirical likelihood and its applications

Two-sample nonparametric test for proportional reversed hazards

In the last few decades, several works have been undertaken in the context of proportional reversed hazard rates (PRHR) but any specific statistical methodology for the PRHR hypothesis is absent in the literature. This paper proposes a two-sample nonparametric test based on two independent samples to verify the PRHR assumption. Based on a consistent U-statistic three statistical methodologies have been developed exploiting U-statistics theory, jackknife empirical likelihood and adjusted jackknife empirical likelihood method. A simulation study has been performed to assess the merit of the proposed test procedure. Finally, the proposed procedure is applied to a data set in the context of brain injury-related biomarkers and a data set related to Duchenne muscular dystrophy.

Penalized Jackknife Empirical Likelihood in High Dimensions

Penalized Jackknife Empirical Likelihood in High Dimensions

Jackknife empirical likelihood ratio test for testing mean time to failure order

Jackknife empirical likelihood ratio test for testing mean time to failure order

A review of recent advances in empirical likelihood

AbstractEmpirical likelihood is widely used in many statistical problems. In this article, we provide a review of the empirical likelihood method, due to its significant development in recent years. Since the introduction of empirical likelihood, variants of empirical likelihood have been proposed, and the applications of empirical likelihood in high dimensions have also been studied. It is necessary to summarize the new development of empirical likelihood. In this article, we give a review of the Bayesian empirical likelihood, the bias‐corrected empirical likelihood, the jackknife empirical likelihood, the adjusted empirical likelihood, the extended empirical likelihood, the transformed empirical likelihood, the mean empirical likelihood, and the empirical likelihood with high dimensions. Finally, we have a brief survey of the computation and implementation for empirical likelihood methods.This article is categorized under: Applications of Computational Statistics > Education in Computational Statistics

Jackknife empirical likelihood ratio test for testing mean residual life and mean past life ordering

We propose nonparametric tests for testing mean residual life and mean past life ordering. Asymptotic properties of the proposed test statistics are studied. We also propose Jackknife Empirical Likelihood (JEL) ratio tests for testing mean residual life and mean past life ordering. Some numerical results are presented to evaluate the performance of the proposed tests by comparing them with few competing tests available in the literature. Finally, we illustrate the proposed test procedures using real data sets.

A jackknife empirical likelihood ratio test for strong mean inactivity time order

We propose a nonparametric test for testing strong mean inactivity time (SMIT) order. A jackknife empirical likelihood (JEL) ratio test for testing SMIT order is also developed. Monte Carlo simulation study show that the proposed test has good power against various alternatives. Finally, we illustrate our method using real data sets.

Jackknife empirical likelihood for the mean of a zero-and-one inflated population

In many statistical analysis, a finite population may contain a large proportion of zero-and-one values that make the population distribution severely skew. Confidence intervals based on a normal approximation (NA) for such data may have low coverage probabilities. In this paper, we apply the methods of jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) to discuss the confidence intervals for the mean of zero-and-one inflated population. Asymptotic distributions of the likelihood-type statistics are studied. Simulations are conducted to compare coverage probabilities with other methods under different distributions. Real data is given to illustrate the procedure of proposed methods.

Bayesian jackknife empirical likelihood for the error variance in linear regression models

Variance estimation is fundamental in the statistical inference. Due to the nonlinearity of the variance estimator, Lin et al. [Jackknife empirical likelihood for the error variance in linear models. J Nonparametr Stat. 2017;29:151–166.] proposed the jackknife empirical likelihood method for the error variance in a linear regression model. However, people may have some prior information about the error variance. In this article, we propose the Bayesian jackknife empirical likelihood (BJEL) for the error variance in a linear regression model. The validity of the proposed method is verified, and the asymptotic normal properties for the BJEL are also established. A simulation study shows that the new approach for the small sample performs better than its frequentist counterpart. Two real data sets are also used to illustrate the proposed methods.

Empirical likelihood and uniform convergence rates for dyadic kernel density estimation

This paper studies the asymptotic properties of and alternative inference methods for kernel density estimation (KDE) for dyadic data. We first establish uniform convergence rates for dyadic KDE. Secondly, we propose a modified jackknife empirical likelihood procedure for inference. The proposed test statistic is asymptotically pivotal regardless of presence of dyadic clustering. The results are further extended to cover the practically relevant case of incomplete dyadic data. Simulations show that this modified jackknife empirical likelihood-based inference procedure delivers precise coverage probabilities even with modest sample sizes and with incomplete dyadic data. Finally, we illustrate the method by studying airport congestion in the United States.

An application of the interval estimation for the At-Risk-of-Poverty Rate assessment

In the document [Eurostat (Your Key to European Statistics) 2020], At-Risk-of-Poverty Rate (ARPR in short) is defined as the percentage of population with an income not exceeding 60% of the general population median income. Extensive and thorough research on the estimation of this measure has been conducted since its introduction. For example, in the paper of [Zieliński 2009a] a non-parametric, distribution-free confidence interval for ARPR has been constructed. An example of application of the confidence interval proposed by [Zieliński 2009a] has been given in [Zieliński 2009b]. Some other interesting approach regarding the interval estimation of ARPR has been proposed in [Luo and Qin 2017], where the authors introduced new concepts of the interval estimation for the so-called Low-Income Proportion (LIP) measure, which is a generalization of ARPR. The LIP measure and thus, the ARPR parameter in particular, are important indexes describing the inequality in an income distribution. Based on the construction of the point smoothed kernel estimate for LIP, [Luo and Qin 2017] established a smoothed jackknife empirical likelihood approach leading to the introduction of some new non-parametric confidence intervals for the LIP measure and consequently, for the ARPR index as well. In our work, we aim to apply the most interesting ideas of LIP and ARPR point and interval estimation for data consisting of observations concerning an equalised disposable income of households in Poland from 2003. We also discuss the accuracy and adequacy of the empirical results relating to the ARPR interval estimation, obtained by the implementation of the constructed confidence intervals.

Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices

Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices