Title: Empirical likelihood in high dimensionality with application to TAAG
Authors: Tongtong Wu - University of Rochester (United States) [presenting]
Cheng Yong Tang - Temple University (United States)
Jinyuan Chang - University of Melboue (Austria)
Abstract: Empirical likelihood (EL) methods, a nonparametric counterpart of likelihood methods, are appealing and effective, especially in conjunction with estimating equations through which useful information can be adaptively and flexibly incorporated. It is also known in the literature that EL approaches encounter substantial difficulties when dealing with problems having high-dimensional model parameters and estimating equations. To answer the challenges, we propose a new penalized EL by applying two penalty functions respectively on the model parameters and the associated Lagrange multipliers in the optimizations of EL. Allowing both the dimensionalities of model parameters and estimating equations growing exponentially with the sample size, the estimator from our new penalized EL is sparse and consistent with asymptotically normally distributed nonzero components. We also design a statistical inference procedure for low-dimensional components of the model parameters, by linearly mapping the original estimating equations to a low-dimensional space. Nest coordinate descent algorithm, along with additional steps, can be used to tackle the well-known difficulties in EL computation, especially in high-dimensional settings. Simulation studies provide numeric evidence that the new penalized EL works well in high dimensionality. This method was applied to the TAAG data to examine multi-level factors related to the MVPA levels over time for girls from adolescence into young adulthood.