Empirical likelihood is a nonparametric method in statistical inference. It profiles a multinomial likelihood supported on the sample without imposing any prior assumption on the shape of confidence regions. In this thesis, we introduce the empirical likelihood method into a two-sample problem, in which two independent and identically distributed samples are independently drawn from two unspecified distributions. The underlying model of the two-sample problem is a location-scale model, F (t) = G ((t - μ) / σ), which involves the location parameter μ and the scale parameter σ. The purpose of this thesis is to make an inference on a vector parameter of interest θ̰ = (μ, σ²). It is shown that the empirical log-likelihood ratio has an asymptotic chi-squared distribution with 2 degrees of f...[ Read more ]

Empirical likelihood is a nonparametric method in statistical inference. It profiles a multinomial likelihood supported on the sample without imposing any prior assumption on the shape of confidence regions. In this thesis, we introduce the empirical likelihood method into a two-sample problem, in which two independent and identically distributed samples are independently drawn from two unspecified distributions. The underlying model of the two-sample problem is a location-scale model, F (t) = G ((t - μ) / σ), which involves the location parameter μ and the scale parameter σ. The purpose of this thesis is to make an inference on a vector parameter of interest θ̰ = (μ, σ²). It is shown that the empirical log-likelihood ratio has an asymptotic chi-squared distribution with 2 degrees of freedom. The result is the nonparametric version of Wilks's theorem in the two-sample location-scale problem. A simulation study assessing performances of empirical likelihood confidence regions and normal approximation confidence regions is also presented. Finally, two further improvements: Bartlett correction and profile empirical likelihood are briefly discussed.