English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Statistical methods with empirical likelihood (EL) are appealing andeffective especially in conjunction with estimating equations through whichuseful data information can be adaptively and flexibly incorporated. It is alsoknown in the literature that EL approaches encounter difficulties when dealingwith problems having high-dimensional model parameters and estimatingequations. To overcome the challenges, we begin our study with a carefulinvestigation on high-dimensional EL from a new scope targeting at estimating ahigh-dimensional sparse model parameters. We show that the new scope providesan opportunity for relaxing the stringent requirement on the dimensionality ofthe model parameter. Motivated by the new scope, we then propose a newpenalized EL by applying two penalty functions respectively regularizing themodel parameters and the associated Lagrange multipliers in the optimizationsof EL. By penalizing the Lagrange multiplier to encourage its sparsity, we showthat drastic dimension reduction in the number of estimating equations can beeffectively achieved without compromising the validity and consistency of theresulting estimators. Most attractively, such a reduction in dimensionality ofestimating equations is actually equivalent to a selection among thosehigh-dimensional estimating equations, resulting in a highly parsimonious andeffective device for high-dimensional sparse model parameters. Allowing boththe dimensionalities of model parameters and estimating equations growingexponentially with the sample size, our theory demonstrates that the estimatorfrom our new penalized EL is sparse and consistent with asymptotically normallydistributed nonzero components. Numerical simulations and a real data analysisshow that the proposed penalized EL works promisingly.

A new scope of penalized empirical likelihood with high-dimensional estimating equations