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USING L2 ESTIMATION FOR L1 ESTIMATORS: AN APPLICATION TO THE SINGLE-INDEX MODEL
Authors:Robert Pari  Sangit Chatterjee
Abstract:The bootstrap method is used to compute the standard error of regression parameters when the data are non-Gaussian distributed. Simulation results with L1 and L2 norms for various degrees of “non-Gaussianess” are provided. The computationally efficient L2 norm, based on the bootstrap method, provides a good approximation to the L1 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.
Keywords:Linear Statistical Models  Portfolio Analysis  Statistcal Techniques
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