  This paper complements the results of Andresen et. al "Critical dimension in
profile semiparametric estimation" (2014) on profile estimators in
semiparametric models. We present two examples. One that illustrates that the
smoothness constraint on the expected value of the contrast functional used to
define the profile M-estimator is necessary for the bound derived for the
critical ratio of dimension to sample size. A second one to show that in the
case that the target dimension is proportional to the full dimension the
critical ratio for the Fisher type result stays the same while for the Wilks
phenomenon it is multiplied with the square root of the full dimension, just as
in the upper bound in Andresen et. al (2014).
