  For a regression model, we consider the risk of the maximum likelihood
estimator with respect to $\alpha$-divergence, which includes the special cases
of Kullback-Leibler divergence, Hellinger distance and $\chi^2$ divergence. The
asymptotic expansion of the risk with respect to the sample size $n$ is given
up to the order $n^{-2}$. We are interested in how the risk convergence speed
(to zero) is affected by the error term distributions of the regression model
and the magnitude of the joint moments of the standardized explanatory
variables. Besides the general result (which is given by Mathematica program),
we consider three concrete error term distributions; a normal distribution, a
t-distribution and a skew-normal distribution. We use the (approximated) risk
of m.l.e. as a measure of the difficulty of estimation for the regression
model. Especially comparing the value of the (approximated) risk with that of a
binomial distribution, we can give a certain standard for the sample size
required to estimate the regression model.
