Reduce computation in profile empirical likelihood method

Li, Minqiang; Peng, Liang; Qi, Yongcheng

doi:10.1002/cjs.10101

Cited by 18 publications

(13 citation statements)

References 41 publications

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“…However, this does not lead to a chi-squared limit due to the plug-in estimator, but rather a weighted sum of independent chi-squared variables, see Chen and Van Keilegom (2009). Recently a jackknife empirical likelihood method was proposed by Jing, Yuan, and Zhou (2009) to deal with non-linear functionals, and Li, Peng, and Qi (2011) employed this idea to reduce the computation of the empirical likelihood method based on estimating equations. Here, we employ the jackknife empirical likelihood method.…”

Section: Jackknife Empirical Likelihood Methodsmentioning

confidence: 99%

Uniform interval estimation for an AR(1) process with AR errors

Hill¹,

Peng

2017

STAT SINICA

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An empirical likelihood method was proposed in Hill and Peng (2014) to construct a unified interval estimation for the coefficient in an AR(1) model, regardless of whether the sequence was stationary or near integrated. The error term, however, was assumed independent, and this method fails when the errors are dependent. Testing for a unit root in an AR(1) model has been studied in the literature for dependent errors, but existing methods cannot be used to test for a near unit root. In this paper, assuming the errors are governed by an AR(p) process, we exploit the efficient empirical likelihood method to give a unified interval for the coefficient by taking the structure of errors into account. Furthermore, a jackknife empirical likelihood method is proposed to reduce the computation of the empirical likelihood method when the order in the AR errors is not small. A simulation study is conducted to examine the finite sample behavior of the proposed methods.

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Section: Jackknife Empirical Likelihood Methodsmentioning

confidence: 99%

Uniform interval estimation for an AR(1) process with AR errors

Hill¹,

Peng

2017

STAT SINICA

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“…• Reduce the computation of U -type profile empirical likelihood. Li et al [6] and Peng [14] considered procedures based on a jackknife plug-in empirical likelihood to save the computation time. We may develop similar procedures to deal with U -structured empirical likelihood.…”

Section: Resultsmentioning

confidence: 99%

“…Wilks' theorems for one and two-sample U -statistics are established. This approach has attracted statisticians' strong interest in a wide range of fields due to its efficiency, and many papers are devoted to the investigation of the method, for example, [9], [14], [2], [22], [23], [7], [6] and so on. However, theorems derived in [4] are limited to a simple case of the Ustatistic but the Gini correlation cannot be estimated by a U -statistic, which does not allow us to apply the results of [4] directly.…”

Section: Introductionmentioning

confidence: 99%

Jackknife empirical likelihood methods for Gini correlations and their equality testing

Sang

Dang

Zhao

2019

Journal of Statistical Planning and Inference

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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. noindent

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“…• Reduce the computation of U -type profile empirical likelihood. Li, Peng and Qi ( [16]) and Peng ([26]) considered procedures based on a jackknife plug-in empirical likelihood to save the computation time. We may develop similar procedures to deal with U -structured empirical likelihood using the robust JEL.…”

Section: Resultsmentioning

confidence: 99%

“…The depth they used is defined as 1/(1 + E F x − X ), which is not robust in terms of unbounded influence function and 0 breakdown point. Nevertheless, we can use Theorem 3.1 of Jiang et al [12], from which the constant c in Theorem 2.1 or Theorem 2.2 can be determined by equation (16).…”

Section: Depth-based Weightsmentioning

confidence: 99%

Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations

Sang

Dang

Zhao

2019

TEST

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In many applications, parameters of interest are estimated by solving some non-smooth estimating equations with U -statistic structure. Jackknife empirical likelihood (JEL) approach can solve this problem efficiently by reducing the computation complexity of the empirical likelihood (EL) method. However, as EL, JEL suffers the sensitivity problem to outliers. In this paper, we propose a weighted jackknife empirical likelihood (WJEL) to tackle the above limitation of JEL. The proposed WJEL tilts the JEL function by assigning smaller weights to outliers. The asymptotic of the WJEL ratio statistic is derived. It converges in distribution to a multiple of a chi-square random variable. The multiplying constant depends on the weighting scheme. The self-normalized version of WJEL ratio does not require to know the constant and hence yields the standard chi-square distribution in the limit. Robustness of the proposed method is illustrated by simulation studies and one real data application. maximization problem of the EL with nonlinear constraints to the simple case of EL on the mean of jackknife pseudo-values, which is very effective in handling one and two-sample U -statistics. Since then, it has attracted strong interests in a wide range of fields due to its efficiency, and many papers are devoted to the investigation of the method, for example, Liu, Xia and Zhou ([20]), Peng ([26]), ([30]) and so on. In many nonparametric and semiparametric approaches, such as the Gini correlation, quantile regression and rank regression, the parameters of interest are estimated by solving equations with U -statistic structure instead of directly by U -statistics. Thus, the JEL in Jing, Yuan and Zhou ([11]) can not be applied directly. Li, Xu and Zhou ([17]) extended the JEL to the more complicated but more general situation. The Wilks' theorems are established even for the situation in which nuisance parameters are involved.As the EL method is sensitive to outliers and the EL confidence regions may be greatly lengthened in the directions of the outliers (Owen[25], Tsao and Zhou[36]), the JEL method with equation constraints is sensitive to outliers. That is, the JEL method is not robust. For the EL approach, a number of methods have been proposed to achieve robustness, see Wu ([42]), Glenn and Zhao ([8]), Jiang et al. ([12]). Those robust empirical likelihood (REL) methods tilt the EL function by assigning smaller weights to outliers, which yield a more robust estimator and confidence region. Jiang et al. ([12]) linked the depth-based weighted empirical likelihood (WEL) with general estimating equations and produced a robust estimation of parameters. They constructed weights based on a depth function although it is not the spatial depth as they claimed. Data depth provides a centre-outward ordering of multi-dimensional data. Points deep inside the data are assigned with a high depth and those on the outskirts with a lower depth. In the literature, depth functions have been extensively studied, for example, Mahalanobis depth ([28]), ...

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Reduce computation in profile empirical likelihood method

Cited by 18 publications

References 41 publications

Uniform interval estimation for an AR(1) process with AR errors

Uniform interval estimation for an AR(1) process with AR errors

Jackknife empirical likelihood methods for Gini correlations and their equality testing

Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations

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