Empirical Bayes Regression Analysis with Many Regressors but Fewer Observations
In this paper, we consider the prediction problem in multiple linear regression model in which the number of predictor variables, p, is extremely large compared to the number of available observations, n. The least squares predictor based on a generalized inverse is not efficient. It is shown that no more than n predictor variables, or n linear combinations of the p predictor variables may be needed for any efficient prediction. We propose six empirical Bayes estimators of the regression parameters used for prediction. Three of them are shown to have uniformly lower prediction error than the least squares predictors when the vector of regressor variables are assumed to be random with mean vector zero and the covariance matrix (1/n)XtX where Xt = (x1, . . . , xn) is the p ~n matrix of observations on the regressor vector centered from their sample means. For other estimators, we use simulation to show its superiority over the least squares predictor.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||Sep 2004|
|Date of revision:|
|Contact details of provider:|| Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033|
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2004cf300. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office)
If references are entirely missing, you can add them using this form.