A Jackknife empirical likelihood approach forK‐sample Tests

Abstract

The categorical Gini correlation is an alternative measure of dependence between categorical and numerical variables, which characterizes the independence of the variables. A non‐parametric test based on the categorical Gini correlation for the equality of K distributions is developed. By applying the jackknife empirical likelihood approach, the standard limiting chi‐squared distribution with degrees of freedom of K − 1 is established and is used to determine the critical value and p‐value of the test. Simulation studies show that the proposed method is competitive with existing methods in terms of power of the tests in most cases. The proposed method is illustrated in an application on a real dataset.

Empirical likelihood test for diagonal symmetry

“…One intuitive explanation is that the JEL approach assigns more weights on the sample points close to 0 and hence the JEL loses some power to reject the symmetry. The same reason leads to low powers for the JEL test in detecting location differences of two distributions [29]. Such a phenomenon is also common for the tests based on the density function approach, as mentioned in [19].…”

“…The JEL has been proved very efficient in dealing with U -statistics and has attracted statistician's interest due to the efficiency. In the literature, there are a quantity of papers utilizing the JEL to conduct tests, see [28], [29], [18], [38] and so on.…”

A review of recent advances in empirical likelihood

“…In addition, the JEL method has been applied in many other aspects, such as, tests for distribution functions (Feng & Peng, 2012a), error distributions in regression models (Feng & Peng, 2012b), the mean absolute deviation (Zhao et al, 2015), the error variance in linear regression models (Lin et al, 2017), the error variance in linear errors‐in‐variables models (Liu & Liang, 2017), the accelerated failure time model (Bouadoumou et al, 2015; Yu & Zhao, 2019b), two high‐dimensional means (Wang et al, 2013), copulas (Peng et al, 2012; Peng & Qi, 2010), Spearman's Rho (Wang & Peng, 2011), the regression imputation and the survey data (Zhong & Chen, 2014), reducing the computation in JEL (Li et al, 2011; Peng, 2012; Zhang et al, 2012), the Pietra ratio (Zhao, Su, & Yang, 2020), multiply robust estimation with missing data (Chen & Haziza, 2018), the mean difference of two zero‐inflated skewed populations (Satter & Zhao, 2021), the high‐dimensional linear regression model (Zang et al, 2016), the equality of variances (Chen, Ning, & Gupta, 2015; Sang, 2021), and K sample test (Sang et al, 2021). An advantage of the JEL method is the simplicity since it just applies the EL method to the sample mean of the jackknife pseudo‐values.…”

Asymptotic Normality of Gini Correlation in High Dimension with Applications to the K-sample Problem

“…All those distance-based tests require a permutation procedure to determine the critical values. Sang, Dang and Zhao [23] developed a nonparametric test applying the jackknife empirical likelihood which has a standard limiting chi-squared distribution. Other tests viewing the K-sample test as an independent test between a numerical and categorical variable can be found in [4,15,32].…”