The use of prior information in linear regression

Abstract

This paper considers the incorporation of previously obtained data with present data from the model Y=Xp+e wnere e˜N(o.e) and b N(b,V) to construct an estimate for the present value of cs. The estimator deiived from combining these two sets or data Is biased, hence its mean square error is compared with the covariance matrix of the Gauss-Markov estimator using only present data. The probability that the combined data yields a better estimator is evaluated. For special cases, che optimal design procedures are presented for obtaining both sets of data.

Keywords:

• Gauss-Markov estimation
• combined estimators
• prior information