Bayesian shrinkage prediction for the regression problem

Details Bayesian shrinkage prediction for the regression problem Bayesian shrinkage prediction for the regression problem

2007-01-21

arxiv.org/abs/math/0701583v1

Mathematics

Statistics Theory

Scientific paper

We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the unknown mean is fixed, the covariance of future samples can be different from training samples. We show that the Bayesian predictive distribution based on the uniform prior is dominated by that based on a class of priors if the prior distributions for the covariance and future covariance matrices are rotation invariant. Then, we consider a class of priors for the mean parameters depending on the future covariance matrix. With such a prior, we can construct a Bayesian predictive distribution dominating that based on the uniform prior. Lastly, applying this result to the prediction of response variables in the Normal linear regression model, we show that there exists a Bayesian predictive distribution dominating that based on the uniform prior. Minimaxity of these Bayesian predictions follows from these results.

Affiliated with

Also associated with

No associations

Rating

Bayesian shrinkage prediction for the regression problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bayesian shrinkage prediction for the regression problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bayesian shrinkage prediction for the regression problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375352