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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 effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a factor that is nearly n\u22121 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.<\/jats:p>","DOI":"10.1111\/rssb.12108","type":"journal-article","created":{"date-parts":[[2015,2,16]],"date-time":"2015-02-16T04:38:18Z","timestamp":1424061498000},"page":"193-210","source":"Crossref","is-referenced-by-count":97,"title":["The Lasso for High Dimensional Regression with a Possible Change Point"],"prefix":"10.1093","volume":"78","author":[{"given":"Sokbae","family":"Lee","sequence":"first","affiliation":[{"name":"Seoul National University , Republic of Korea"},{"name":"Institute for Fiscal Studies , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Myung Hwan","family":"Seo","sequence":"additional","affiliation":[{"name":"London School of Economics and Political Science , UK"},{"name":"Seoul National University , Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Youngki","family":"Shin","sequence":"additional","affiliation":[{"name":"University of Western Ontario , London , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2015,2,15]]},"reference":[{"key":"2023021709313059300_rssb12108-cit-0001","volume-title":"Data set for a panel of 139 countries","author":"Barro","year":"1994"},{"key":"2023021709313059300_rssb12108-cit-0002","volume-title":"Economic Growth","author":"Barro","year":"1995"},{"key":"2023021709313059300_rssb12108-cit-0003","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1214\/10-AOS827","article-title":"l1-penalized quantile regression in high-dimensional sparse models","volume":"39","author":"Belloni","year":"2011","journal-title":"Ann. 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