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USING L 2 ESTIMATION FOR L 1 ESTIMATORS: AN APPLICATION TO THE SINGLE‐INDEX MODEL
Author(s) -
Pari Robert,
Chatterjee Sangit
Publication year - 1986
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1986.tb00234.x
Subject(s) - estimator , standard error , gaussian , ordinary least squares , mathematics , statistics , index (typography) , norm (philosophy) , computer science , regression , estimation , mathematical optimization , economics , physics , quantum mechanics , world wide web , political science , law , management
The bootstrap method is used to compute the standard error of regression parameters when the data are non‐Gaussian distributed. Simulation results with L 1 and L 2 norms for various degrees of “non‐Gaussianess” are provided. The computationally efficient L 2 norm, based on the bootstrap method, provides a good approximation to the L 1 norm. The methodology is illustrated with daily security return data. The results show that decisions can be reversed when the ordinary least‐squares estimate of standard errors is used with non‐Gaussian data.