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Introduction
Published in Bradley Efron, R.J. Tibshirani, An Introduction to the Bootstrap, 1994
Bradley Efron, R.J. Tibshirani
Attractive properties of the empirical likelihood include: a) it transforms as a likelihood should [the empirical likelihood of g(θ) is Lemp(g(θ)) ], and b) it is defined only for permissible values of θ, (for example [-1,1] for a correlation coefficient). A further advantage of empirical likelihood is its simple extension to multiple parameters of interest. This feature is not shared by most of the other techniques described in this chapter.
Penalized Empirical Likelihood-Based Variable Selection for Longitudinal Data Analysis
Published in American Journal of Mathematical and Management Sciences, 2021
Tharshanna Nadarajah, Asokan Mulayath Variyath, J Concepción Loredo-Osti
The empirical likelihood (EL) is a nonparametric method for statistical inference; that is, we need not assume that the data come from a particular distribution. The EL combines the reliability of nonparametric methods with the flexibility and effectiveness of the likelihood approach. The EL has many nice properties parallel to those of parametric likelihood, including the ability to carry out hypothesis tests and constructs confidence intervals without estimating the variance. The shape of EL confidence regions automatically reflects the emphasis of the observed data set. These regions are invariant under transformations and often behave better than confidence regions based on asymptotic normality when the sample size is small. The EL method also offers advantages in parameter estimation and the formulation of goodness-of-fit tests. Moreover, it is possible to have more estimating equations than the number of parameters, i.e., r > p, where is an estimating function for the parameter The EL has been successfully applied in areas such as linear models, GLMs, survey sampling, variable selection, survival analysis, and time series.