A Progressive Block Empirical Likelihood Method for Time Series

• 成果类型: Article
• 署名作者: Kim, Young Min; Lahiri, Soumendra N.; Nordman, Daniel J.
• 署名单位: Radiation Effects Research Foundation - Japan; North Carolina State University; Iowa State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.847374
• 发表日期: 2013
• 页码: 1506-1516
• 关键词: general estimating equations; weakly dependent processes; euclidean likelihood; MOMENTS ESTIMATION; bootstrap; ratio; temperature; statistics; variance; models

摘要

This article develops a new blockwise empirical likelihood (BEL) method for stationary, weakly dependent time processes, called the progressive block empirical likelihood (PBEL). In contrast to the standard version of BEL, which uses data blocks of constant length for a given sample size and whose performance can depend crucially on the block length selection, this new approach involves a data-blocking scheme where blocks increase in length by an arithmetic progression. Consequently, no block length selections are required for the PBEL method, which implies a certain type of robustness for this version of BEL. For inference of smooth functions of the process mean, theoretical results establish the chi-squared limit of the log-likelihood ratio based on PBEL, which can be used to calibrate confidence regions. Using the same progressive block scheme, distributional extensions are also provided for other nonparametric likelihoods with time series in the family of Cressie-Read discrepancies. Simulation evidence indicates that the PBEL method can perform comparably to the standard BEL in coverage accuracy (when the latter uses a good block choice) and can exhibit more stability, without the need to select a usual block length. Supplementary materials for this article are available online.