  A natural (yet unconventional) test for goodness-of-fit measures the
discrepancy between the model and empirical distributions via their Euclidean
distance (or, equivalently, via its square). The present paper characterizes
the statistical power of such a test against a family of alternative
distributions, in the limit that the number of observations is large, with
every alternative departing from the model in the same direction. Specifically,
the paper provides an efficient numerical method for evaluating the cumulative
distribution function (cdf) of the square of the Euclidean distance between the
model and empirical distributions under the alternatives, in the limit that the
number of observations is large. The paper illustrates the scheme by plotting
the asymptotic power (as a function of the significance level) for several
examples.
