A penalized empirical likelihood method in high dimensions

By Soumendra Nath Lahiri, S. Mukhopadhyay. 2013

53 citations recorded by the source corpus.

This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure, and it is typically different from the usual chi-squared limit of the empirical likelihood ratio statistic in the fixed and finite dimensional case. A unified subsampling based calibration is proposed, and its validity is established in all three cases, (i)-(iii). Finite sample properties of the method are investigated through a simulation study.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c884470a3353afa5cc43fab6d29559a7e1aecb2b

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Citations in the corpus

High dimensional generalized empirical likelihood for moment restrictions with dependent data (2013, methodology): “For GEL, we define the GEL ratio as wn(θ) = 2ρvv(0) ρ2v(0) { Qρ(0)− max λ∈Λ̂n(θ) Q∑ q=1 ρ(λ′φq(θ)) } (19) which is the extension of the EL ratio in the GEL framework.”
Empirical likelihood on the full parameter space (2013, background): “Recently, Lahiri and Mukhopadhyay (2012) showed that under certain dependence structures, a modified PEL for the mean works in the extremely difficult case of large dimension and small sample size.”