Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/111379 
Year of Publication: 
2014
Series/Report no.: 
cemmap working paper No. CWP26/14
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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.
Subjects: 
Lasso
oracle inequalities
sample splitting
sparsity
threshold models
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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