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Activity Number: 57 - Some Recent Developments and Applications of the Empirical Likelihood Method
Type: Topic Contributed
Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
Sponsor: International Chinese Statistical Association
Abstract #323268
Title: A New Scope of Penalized Empirical Likelihood with High-Dimensional Estimating Equations
Author(s): Chengyong Tang* and Jinyuan Chang and Tong Tong Wu
Companies: Temple University and Southwestern University of Finance and Economics and University of Rochester
Keywords: Empirical likelihood ; Estimating equations ; Moment selection ; Penalized likelihood

Statistical inferences with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations through which useful data information can be adaptively and flexibly incorporated. It is also known in the literature that EL approaches encounter difficulties when dealing with problems having high-dimensional model parameters and estimating equations. To overcome the challenges, we consider in this study a new penalized EL approach. We propose to apply two penalty functions respectively regularizing the model parameters and the associated Lagrange multipliers in the optimizations of EL. By penalizing the Lagrange multiplier to encourage its sparsity, we show that drastic dimension reduction in the number of estimating equations can be achieved in EL. Most attractively, such a reduction in dimensionality of estimating equations is actually equivalent to a selection among those high-dimensional estimating equations, resulting in a highly parsimonious and effective device for high-dimensional sparse model parameters. Allowing both dimensionalities of model parameters and estimating equations growing exponentially with the sample size, our theory demon

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