Empirical likelihood in a semi-parametric model

Sometimes we cannot specify a statistical model in a parametric form completely, For example, we might assume that a random variable has a distribution that is roughly normal in the centre of the distribution but with tails that are arbitrary, We might then be interested in inference for the mean of the distribution, using methods that are insensitive to the shape of the tails. In this paper, we define the semi-parametric likelihood function. We show that the semi-parametric likelihood ratio statistic has asymptotically a chi-squared distribution. Some simulation results are presented.