Strong consistency of the MLE for sequential design problems (Q1118955)

The authors prove strong consistency of the maximum likelihood estimator for compact experiment spaces under some conditions on the integrability of the likelihood ratio. In particular, their result implies strong consistency of the MLE for the parameter \(\tau =\theta_ 1/2 \theta_ 2\) in the regression model \(y_ i=\theta x_ i+\theta_ 2x^ 2_ i+e_ i\) with \(| x_ i| \leq 1\) and where \(e_ i\) are i.i.d. N(0,1).