The Experience Of Semi-parametric Model The Likelihood Of Statistical Inference

The empirical likelihood method of Owen (1988) is a nonparametric method of inference. The method gains an advantage over the classical or the modern. The semiparametric regress model is important model developed in 1980's. It colligates the merits of regress model and nonparametric model. Therefore it has strong application property.In this paper, we consider the application of the empirical likelihood method to semiparametric model:wherex_i = (x_i1,x_i2,…,x_ik)'is non-random design variable, β = (β₁,β₂,…,β_k)'is the unknown parameter, g(·)is the unknown real-valued function on R^k, e_i is therandom error variable with Ee_i =0, Ee_i² =σ² <∞, a nonparametric version of theWilks theorem is derived. The result is used to construct the confidence region of parameter vector. Consider the application of the empirical likelihood method to the Errors-In-Variables semiparametric Regress Model:Where X_i is the k-dimensional vector can't be observed, x_i is the k-dimensional vector can be observed, δ_i is the random error variable with Eδ_i, = 0,. We prove that the empirical log-likelihood isasymptotic chi-square distribution.