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Empirical Likelihood
Published in Albert Vexler, Alan D. Hutson, Xiwei Chen, Statistical Testing Strategies in the Health Sciences, 2017
Albert Vexler, Alan D. Hutson, Xiwei Chen
The empirical likelihood method for constructing confidence regions for parameters, expressed as functionals θ(F) of an unknown distribution function F, introduced by Owen (1988, 1990) has sampling properties similar to those of the bootstrap. While the bootstrap uses resampling, the empirical likelihood method computes the profile likelihood of a general multinomial distribution based on data points. In a two-sample problem where one sample comes from a distribution specified up to a parameter and the other sample comes from an unspecified distribution, Qin (1991) generalized Owen’s empirical likelihood and provided a likelihood ratio–based confidence interval for the difference of two sample means. Qin (1993) introduced empirical likelihood in the biased sampling problem. Wilks’ theorem leading to an empirical likelihood ratio confidence interval for the mean, as well as some extensions, discussion, and simulations, was presented.
Rewiring of miRNA-mRNA bipartite co-expression network as a novel way to understand the prostate cancer related players
Published in Systems Biology in Reproductive Medicine, 2023
Mohammad Mehdi Naghizadeh, Behnaz Bakhshandeh, Farshid Noorbakhsh, Marjan Yaghmaie, Ali Masoudi-Nejad
When g, l, and f were the number of gained, lost, and fixed edges of each node during a change from normal to cancer state, then the probability of this state was computed as below: e = g + l + f and pg = g/e, pl = l/e, pf = f/e. Under the null hypothesis, the probability of G, L, and F was computed as pG = G/E, pL = L/E, pF = F/E from the total edges of the rewiring network. According to Wilks’ theorem -2ln(likelihood for null model/likelihood of alternative model) has a chi-square distribution with dfalt-dfnul degree of distribution. We also adjusted the p-values of the chi-square test with FDR to avoid a false positive.
Distribution of the C statistic with applications to the sample mean of Poisson data
Published in Journal of Applied Statistics, 2020
For Poisson data, W. Cash [9] showed that the Wilks theorem can be used to generate confidence intervals for interesting parameters from the statistic approximately distributed like a 2) with a fixed model 2.2. Unlike N and μ, and therefore critical values must be estimated via Monte Carlo simulations of Equation (19) as a function of N and μ.