A New Approach to Variance Estimation for Time-Ordered Dependent Data

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Molly M. Davies*+ and Mark J. van der Laan
• Companies: University of California, Berkeley and University of California, Berkeley
• Keywords: time series ; inference ; influence functions ; semiparametric ; jackknife ; weak dependence

Abstract

Suppose we have a data set of n time-ordered observations where the extent of dependence between them is poorly understood. We assume we have an estimator that is consistent for a particular estimand at a known rate, and the dependence structure is weak enough so that the standardized estimator is asymptotically normally distributed. Our goal is to estimate the asymptotic variance of the standardized estimator so that we can construct a Wald-type confidence interval for the estimand. In this paper we consider an approach that allows us to learn this asymptotic variance from a sequence of influence function based estimators. We show that our approach is consistent, and evaluate its practical performance with a simulation study. Our simulation results show that our method compares favorably with various subsampling and bootstrap approaches. We also demonstrate how our method can be used with an m-dependent jackknife variance estimator.