Empirical likelihood for a semiparametric regression model
Tao Cheng · Basic Sciences Journal of Textile Universities · 2010
The application of semiparametric regression model yi=xi′ β+g(xi)+ei,1≤i≤n is considered,where xi=(xi1,xi2,…,xik)′ is non-random design variables,β=(β1,β2,…,βk)′ is unknown parameter,g(·) is unknown function.ei is random error and E(ei)=0,E(e2i)=σ2∞.At the first,suppose β is known,g is estimated by nonparameter weight functions,then likelihood function is structured by empirical likelihood method.It is proved that the empirical log-likelihood ratio statistic is asymptotically chisquared distribute.The empirical likelihood confidence regions can be constructed accordingly.