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In this paper, we apply empirical likelihood for two-sample problems with growing high dimensionality. Our results are demonstrated for constructing confidence regions for the difference of the means of twop-dimensional samples and the difference in value between coefficients of twop-dimensional sample linear model. We show that empirical likelihood based estimator has the efficient property. That is, asp→ ∞ for high-dimensional data, the limit distribution of the EL ratio statistic for the difference of the means of two samples and the difference in value between coefficients of two-sample linear model is asymptotic normal distribution. Furthermore, empirical likelihood (EL) gives efficient estimator for regression coefficients in linear models, and can be as efficient as a parametric approach. The performance of the proposed method is illustrated via numerical simulations. [ABSTRACT FROM AUTHOR]

The local Walsh-average regression has been shown to be a comparable method to the others in nonparametric regression. In this paper, we develop a new estimation procedure based on local Walsh-average regression for single index varying coefficient models. Under some general assumptions, we establish the asymptotic properties of the proposed estimators for both the parametric and nonparametric parts. We further demonstrate that the proposed estimates have great efficiency gains across a wide spectrum of non-normal error distributions and almost not lose any efficiency for the normal error compared with that of local polynomial regression estimates under the least squares loss. Even in the worst case scenarios, the asymptotic relative efficiency owns a lower bound equaling to 0.864 for estimating the single-index parameter and a lower bound being 0.8896 for estimating the nonparametric link functions respectively, versus the least squares estimators. A simulation study is conducted to assess the finite sample properties of the proposed procedure, and a real data analysis is followed to further illustrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]