The lasso for high-dimensional regression with a possible change-point

Sokbae (Simon) Lee, Myung Hwan Seo and Youngki Shin
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Myung Hwan Seo: Institute for Fiscal Studies
Youngki Shin: Institute for Fiscal Studies

No CWP26/14, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l1 estimation loss for regression coefficients. Since the Lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold e ect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a nearly n-1 factor even when the number of regressors can be much larger than the sample size (n). We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.

Date: 2014-05-28
New Economics Papers: this item is included in nep-ecm
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Journal Article: The lasso for high dimensional regression with a possible change point (2016)
Working Paper: The lasso for high-dimensional regression with a possible change-point (2014)
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