Empirical likelihood methods with weakly dependent processes. (English) Zbl 0881.62095

Kitamura, Yuichi

Ann. Stat. 25, No. 5, 2084-2102 (1997).

Summary: This paper studies the method of empirical likelihood in models with weakly dependent processes. In such cases, if the likelihood function is formulated as if the data process were independent, obviously empirical likelihood fails. We propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner. This method of “blockwise empirical likelihood” preserves the dependence of data, and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals.
We consider general estimating equations, for which an efficient estimator is derived by maximizing blockwise empirical likelihood. We also introduce “blocks-of-blocks empirical likelihood” to conduct inference for parameters of the infinite dimensional joint distribution of data; the smooth function model is used for such cases. We show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is Bartlett correctable. A wide variety of problems, such as time series regressions and spectral densities, can be treated using our methodology.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10	Nonparametric hypothesis testing
62E20	Asymptotic distribution theory in statistics

Keywords:

Bartlett correction; Edgeworth expansion; estimating function; generalized method of moments; nonparametric likelihood; spectral density; strong mixing; time series regression; weak dependence; empirical likelihood