Unbiased Estimation for Linear Regression When n < v

  •  Saeed Aldahmani    
  •  Hongsheng Dai    


In this paper a new method is proposed for solving

the linear regression problem when the number of observations $n$

is smaller than the number of predictors v. This method uses the

idea of graphical models and provides unbiased parameter estimates

under certain conditions, while existing methods such as ridge

regression, LASSO and least angle regression (LARS) give biased

estimates. Also the new method can provide a detailed graphical

correlation structure for the predictors, therefore the real

causal relationship between predictors and response could be

identified. In contrast, existing methods often cannot identify

the real important predictors which have possible causal effects

on the response variable. Unlike the existing methods based on graphical models, the proposed method can identify the potential networks while doing regression even if the data do not follow a multivariate distribution. The new method is compared with some existing methods such as ridge regression, LASSO and LARS by using simulated and real data sets. Our experiments reveal that the new method outperforms all the other methods when n<v.

This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1927-7032
  • ISSN(Online): 1927-7040
  • Started: 2012
  • Frequency: bimonthly

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