Finite-sample performance of convex optimization algorithms in empirical likelihood ratio-based goodness-of-fit test statistics

The finite-sample performance of convex optimization algorithms for the empirical likelihood methodology has been assessed using an empirical likelihood ratio (ELR) based test statistic for normality. Using the R statistical package, a Monte Carlo simulation approach was adopted to compare various f...

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Veröffentlicht in:Journal of statistical computation and simulation Jg. 95; H. 15; S. 3330 - 3352
1. Verfasser: Marange, Chioneso Show
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis 13.10.2025
Schlagworte:
algorithms
Convex optimization
empirical likelihood
goodness-of-fit
normality
ISSN:0094-9655, 1563-5163
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Zusammenfassung:The finite-sample performance of convex optimization algorithms for the empirical likelihood methodology has been assessed using an empirical likelihood ratio (ELR) based test statistic for normality. Using the R statistical package, a Monte Carlo simulation approach was adopted to compare various functions that utilize different algorithms based on the convex optimization theory. The simulation results demonstrated that the Davidon-Fletcher-Powell (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization techniques are the fastest in small to relatively large samples. Though the Newton algorithm for the el.convex package is somewhat faster than the optimization algorithm for the el.test function, these two algorithms are somewhat similar in performance. The damped Newton and the conjugate gradient (FRPR) algorithms were the slowest. The computational performance behavioural patterns are heavily dependent on sample size and the distributional properties of the applied distribution under $ H_0 $ H 0 for the ELR-based test statistic. On the other hand, the total iterations and sum of weights are heavily dependent on the optimization algorithms. In addition, the optimization algorithms do not change the behaviour of the large sample asymptotic property of the studied ELR-based test statistic; that is, no adjustments to the critical values are necessary when using these algorithms. As expected, Type I error rate control and power of the ELR-based test statistic are not affected by the optimization techniques. In conclusion, under certain simulation scenarios, the Newton, BFGS and DFP algorithms found in the el.convex package may be used as alternatives to the traditional optimization algorithm used by the el.test function. Some real data applications are also presented.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2025.2530485