Empirical Likelihood Statistical Inference And Application

Empirical likelihood is a nonparametric method of statistical inference, this paper introduced historical development and present situation of empirical likelihood method, we mainly develop the empirical likelihood method to partially linear error-in-responses models and partially linear regression model missing responses at random, for apply empirical likelihood method to other models, we only introduce simply.First, this paper introduced the defines of empirical likelihood and it application in functions of means, M-estimates, nonparametric regression and uncomplete data, thus let us have an initial knowing about empirical likelihood and help us understand the essence of empirical likelihood.Second, develop the empirical likelihood method and apply it to partially linear error-in-responses models. Error-in-variable had been applied in many areas, for example economy, biology and so on, error-in-responses is a realistic situation too. In this paper, a nonparametric version of Wilks theorem is derived, the result is then used to construct confidence regions of the parameter vector. Confidence regions for (3 can also be constructed using other methods, but the empirical likelihood method is very easy to implement in practice.Finally, extend the empirical likelihood method to partially linear regression model missing responses at random. In fact, missing responses are common in opinion polls, market research surveys, socioeconomic investigations, medical studies and other scientific experiments. The main purpose of this article is to extend the empirical likelihood method to the missing response problem make statistical inferences 6 on the mean of response Y, especially we consider the case where some Y values in a sample of size n may be missing at random (MAR), in this article, statistical inferences 6 on the mean of response Y with some auxiliary informationis available.