Asymptotics for lasso-type estimators

Wenjiang Fu; Keith Knight

doi:10.1214/aos/1015957397

Abstract

We consider the asymptotic behavior ofregression estimators that\nminimize the residual sum of squares plus a penalty proportional to\n$\\sum|\\beta_j|^{\\gamma}$. for some $\\gamma > 0$. These estimators include\nthe Lasso as a special case when $\\gamma = 1$. Under appropriate conditions, we\nshow that the limiting distributions can have positive probability mass at 0\nwhen the true value of the parameter is 0.We also consider asymptotics for\n“nearly singular” designs.

Keywords

MathematicsEstimatorLasso (programming language)Applied mathematicsType (biology)LimitingResidualLeast-squares function approximationAsymptotic distributionM-estimatorStatisticsAlgorithm

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Publication Info

Year: 2000
Type: article
Volume: 28
Issue: 5
Citations: 1312
Access: Closed

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APA Style

                            
                                    Wenjiang Fu, 
                                
                                    Keith Knight
                                
                            (2000). 
                            Asymptotics for lasso-type estimators. 
                            The Annals of Statistics
                            , 28
                            (5)
                            .
                            https://doi.org/10.1214/aos/1015957397

Identifiers

DOI: 10.1214/aos/1015957397