A New Version of Blockwise Empirical Likelihood for Time Series

• Activity Number: 273
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Soumen Lahiri and Dan Nordman*+
• Companies: Texas A&M University and Iowa State University
• Keywords: Data blocks ; Confidence regions ; Functional CLT ; Smooth function parameter

Abstract

This talk will introduce a version of block-based empirical likelihood (EL) for time series, which, unlike the standard version, does not involve any particular block choices. Because the block choice is known to crucially impact the performance of the standard version of blockwise, this new blockwise formulation of EL has a practical advantage in avoiding block selection. Under mild assumptions on the time stationary time process, a non-parametric Wald type result holds for this formulation of blockwise EL where log-EL ratio (evaluated at the true parameter) has well-defined, distribution-free limit, that can be used to calibrate confidence regions. This limit distribution is not chi-squared and hence non-standard, but simulation from the limit law is fairly straightforward. The EL method can be used to calibrate confidence regions for mean parameters or smooth functions of mean parameters. We will examine the performance of the method through simulation and illustrate its use with a real data example.