AN EXTENDED EMPIRICAL LIKELIHOOD FOR GENERALIZED LINEAR MODELS

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High dimensional generalized empirical likelihood for moment restrictions with dependent data (2013, background): “…EL is its resembling the parameter likelihood by have a limiting chi-square distribution under a wide range of situations, as demonstrated in Owen (1988), Chen and Cui (2003), Qin and Lawless (1994) and Chen and Van Keilegom (2009) for independent data, and Kitamura (1997) for dependent data.”
A review on empirical likelihood methods for regression (2009, methodology): “For generalized linear models, Kolaczyk (1994) formulated the EL based on the conditional mean aspect of the model; Chen and Cui (2003) considered adding extra constraints based on the conditional variance information within the GLIM to improve estimation efficiency.”
An updated review of Goodness-of-Fit tests for regression models (2013, background): “…= −2 ∫ log ( Ln ( m̃(x,̂θ)nn )) ω(x)dx, where Ln(m̃(x,̂θ)) = max∏ni=1 pi(x), subject to n ∑ i=1 pi(x) = 1, n ∑ i=1 pi(x)Kh(x − Xi) ( Yi − m̃(x,̂θ) ) = 0 with m̃(x,̂θ) = E ̂θ (mnh(x)) the empirical local likelihood under H0 (see Chen and Cui 2003 and Chen and Van Keilegom 2009b for more details).”