Structural Change in Sparsity

Sokbae Lee; Yuan Liao; Myung Hwan Seo; Youngki Shin

doi:10.48550/arxiv.1411.3062

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Structural Change in Sparsity

Sokbae Lee, Yuan Liao, Myung Hwan Seo and Youngki Shin

ArXiv.org

Cornell University

11/11/2014

DOI: 10.48550/arxiv.1411.3062

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the population and across the individuals in the collected sample. In practice, however, the sparsity structure may not always be invariant in the population, due to heterogeneity across different sub-populations. We consider a general, possibly non-smooth M-estimation framework, allowing a possible structural change regarding the identities of important regressors in the population. Our penalized M-estimator not only selects covariates but also discriminates between a model with homogeneous sparsity and a model with a structural change in sparsity. As a result, it is not necessary to know or pretest whether the structural change is present, or where it occurs. We derive asymptotic bounds on the estimation loss of the penalized M-estimators, and achieve the oracle properties. We also show that when there is a structural change, the estimator of the threshold parameter is super-consistent. If the signal is relatively strong, the rates of convergence can be further improved and asymptotic distributional properties of the estimators including the threshold estimator can be established using an adaptive penalization. The proposed methods are then applied to quantile regression and logistic regression models and are illustrated via Monte Carlo experiments.

Statistics - Methodology

Details

Title: Subtitle: Structural Change in Sparsity
Creators: Sokbae Lee
Yuan Liao - University of Maryland, College Park
Myung Hwan Seo - London School of Economics and Political Science
Youngki Shin - Western University
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.1411.3062
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, NY
Language: English
Date posted: 11/11/2014
Academic Unit: Economics
Record Identifier: 9984937927002771

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