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The information for the direction of dependence in l1 regression
Authors:Yadolah Dodge  Joe Whittaker
Institution:1. Groupe de Statistique , Neuchatel University , 2002, Suisse E-mail: yadolah.dodge@seco.unine.ch;2. Mathematics and Statistics , Lancaster University , LAI 4YF, UK E-mail: joe.whittaker@lancaster.ac.uk
Abstract:Fitting a linear regression for a response variable by minimising the sum of absolute deviations, L1 regression, may be viewed as a maximum likelihood procedure applied to the Laplace distribution. An interesting bivariate case is where the conditional distribution of the response X2 given X1 and the marginal distribution of the explanatory variable X1 are both Laplace. In this context we show there is information to distinguish the direction of dependence between X1 and X2 from observations. That is we may distinguish the model in which X1 is dependent on X2 from that in which X2 is dependent on X1 This is not true for L2 regression based on the Normal distribution.
Keywords:information divergence  Laplace distribution
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