Empirical likelihood (EL) is a method for estimation and inference without making distributional assumptions. Viewed as a nonparametric maximum likelihood estimation procedure (NPMLE), it approximates the unknown distribution function with a discrete distribution, then applies the ML estimation method. Alternatively, EL can be regarded as a minimum divergence estimation procedure. EL works well for estimating moment condition models, though it applies to other models as well. The large deviation principle (LDP) and other techniques show that EL has many optimality properties.
KeywordsBlockwise empirical likelihood Empirical likelihood Empirical likelihood ratio Generalized empirical likelihood Generalized method of moments Kernel regression technique Lagrange multiplier Large deviation principle Maximum likelihood Nonparametric maximum likelihood estimation Semiparametric estimation Vector autoregressions
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