Central Limit Theory for Kernel-Self Normalized Tail-Trimmed Sums of Dependent, Heterogeneous Data with Applications

Although robust estimation methods were formalized by the late 1800s, data trimming and truncation for non-iid data has received little attention. We present Gaussian central limit theorems for tail-trimmed sums of a heavy tailed weakly dependent process in the Feller class. We assume distribution tails are stationary, and otherwise leave stationarity and heterogeneity unrestricted. The sum is self-normalized with a consistent kernel variance estimator, so the rate of convergence, tail thickness and memory persistence do not need to be specified beyond fairly minimal regularity conditions, hence robust inference is available. The theory applies to mixing and non-mixing processes, including linear and nonlinear distributed lags, and linear and nonlinear random volatility with smooth or non-smooth errors. We show how the results imply asymptotic normality for sample tail-trimmed variances and covariances, and a super-p n-convergent least squares estimator for infinite vari