  We consider a linear minimum mean squared error (LMMSE) estimation framework
with model mismatch where the assumed model order is smaller than that of the
underlying linear system which generates the data used in the estimation
process. By modelling the regressors of the underlying system as random
variables, we analyze the average behaviour of the mean squared error (MSE).
Our results quantify how the MSE depends on the interplay between the number of
samples and the number of parameters in the underlying system and in the
assumed model. In particular, if the number of samples is not sufficiently
large, neither increasing the number of samples nor the assumed model
complexity is sufficient to guarantee a performance improvement.
