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Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising new model selection method; this connection explains the similar numerical results previously observed for the Lasso and Stagewise, and helps us understand the properties of both methods, which are seen as constrained versions of the simpler LARS algorithm. (3) A simple approximation for the degrees of freedom of a LARS estimate is available, from which we derive a Cp estimate of prediction error; this allows a principled choice among the range of possible LARS estimates. LARS and its variants are computationally efficient: the paper describes a publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates.<\/jats:p>","DOI":"10.1214\/009053604000000067","type":"journal-article","created":{"date-parts":[[2004,5,27]],"date-time":"2004-05-27T14:15:51Z","timestamp":1085667351000},"page":"407-499","source":"Crossref","is-referenced-by-count":6745,"title":["Least angle regression"],"prefix":"10.1214","volume":"32","author":[{"given":"Bradley","family":"Efron","sequence":"first","affiliation":[{"name":"Department of Statistics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Trevor","family":"Hastie","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iain","family":"Johnstone","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Tibshirani","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"26","doi-asserted-by":"crossref","unstructured":"Breiman, L. 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