The Kernel Self-Normalized, Tail-Trimmed Sum for Dependent, Heterogeneous Data, with an Application to Robust Least Squares

• Activity Number: 361
• Type: Contributed
• Date/Time: Wednesday, August 6, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jonathan B. Hill*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: tail trimmed sum ; Near Epoch Dependence ; mixing ; heavy tails ; robust estimation ; kernel variance

Abstract

Altough robust estimation methods were formalized by the late 19th century, data trimming and truncation for non-iid data has received little attention. We establish sufficient conditions for asymptotic normality of a tail-trimmed sum of dependent, heterogeneous data. The sum is self-standardized with a kernel variance estimator so the rate of convergence, tail thickness and memory persistence do not need to be specified. The resulting central limit theory applies to mixing, geometrically ergodic, and Near-Epoch-Dependent processes in general, including linear and nonlinear distributed lags, FIGARCH and stochastic volatility processes, all with short or long memory and thin or thick-tailed shocks. The theory is applied to asymptotically Gaussian least squares estimation of an infinite variance first-order difference equation.