Empirical likelihood ratio test for or against a set of inequality constraints

doi:10.1016/0378-3758(95)00188-3

Journal of Statistical Planning and Inference

Volume 55, Issue 2, 30 October 1996, Pages 191-204

https://doi.org/10.1016/0378-3758(95)00188-3 Get rights and content

Abstract

We use the empirical likelihood ratio approach introduced by Owen (Biometrika 75 (1988), 237–249) to test for or against a set of inequality constraints when the parameters are defined by estimating functions. Our objective in this paper is to show that under fairly general conditions, the limiting distributions of the empirical likelihood ratio test statistics are of chi-bar square type (as in the parametric case) and give the expression of the weighting values. The results obtained here are similar to those in El Barmi and Dykstra (1995) where a full distributional model is assumed. This work presents also an extension of the results in Qin and Lawless (1995).

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Cited by (18)

Empirical likelihood ratio tests with power one
2018, Statistics and Probability Letters
Citation Excerpt :
Alternatively El Barmi (1996) introduced the retrospective ELR method to test for or against a set of inequality constraints. We implement and refine the methodologies developed by DiCiccio and Romano (1989) and El Barmi (1996) to propose the one-sided ELR sequential tests. This paper is organized as follows.
In the 1970s, Professor Robbins and his coauthors extended the Vile and Wald inequality in order to derive the fundamental theoretical results regarding likelihood ratio based sequential tests with power one. The law of the iterated logarithm confirms an optimal property of the power one tests. In parallel with Robbins’s decision-making procedures, we propose and examine sequential empirical likelihood ratio (ELR) tests with power one. In this setting, we develop the nonparametric one- and two-sided ELR tests. It turns out that the proposed sequential ELR tests significantly outperform the classical nonparametric t-statistic-based counterparts in many scenarios based on different underlying data distributions.
Restricted one way analysis of variance using the empirical likelihood ratio test
2011, Journal of Multivariate Analysis
Empirical likelihood (EL) ratio tests are developed for testing for or against the hypothesis that $k$ -population means $μ_{1}, μ_{2}, \dots, μ_{k}$ are isotonic with respect to some quasi-order $⪯$ on ${1, 2, \dots, k}$ . The null asymptotic distributions are derived and are shown to be of chi-bar squared type. The asymptotic power of the proposed test for testing for equality of these means against the order restriction is derived under contiguous alternatives and a simulation study is carried out to investigate the finite sample behaviors of this test. In addition, an adjusted EL test is used to improve the small size performance of our test and an example is also discussed to illustrate the theoretical results.
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2009, Journal of Econometrics
This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules. The results obtained in this paper extend to conventional GMM estimators.
An appraisal of some aspects of statistical inference under inequality constraints
2002, Journal of Statistical Planning and Inference
Two principal tools, namely, the likelihood and the union-intersection principles are critically appraised with respect to their roles in drawing statistical inference when the parameters are subject to inequality constraints. Parametric, semiparametric, and nonparametric models are reviewed in such nonstandard setups, and statistical resolutions are examined with due respect to applicability, validity, computational flexibility and efficiency considerations.
Order-restricted inference for means with missing values
2017, Biometrics
Hypothesis test on response mean with inequality constraints under data missing when covariables are present
2017, Statistical Papers

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Empirical likelihood ratio test for or against a set of inequality constraints

Abstract

Statist. Probab. Lett.

Orthant probabilities for the quadrivariate normal distribution

Ann. Math. Statist.

Empirical likelihood is Bartlett-correctable

Ann. Statist.

On adjustments to the signed root of the empirical likelihood ratio statistic

Biometrika

Testing for or against a set of linear inequality constraints in a multinomial situation

Canad. J. Statist.

Testing against a set of inequality constraints

Methodology and algorithms of empirical likelihood

Internat. Statist. Rev.

A multivariate analogue of one-sided test

Biometrika