1. In the data set discussed here, the GEC's standard errors are too low essentially because it misjudges the binomial variance in the event counts. The point is most easily seen when xi = 0. In the data themselves, the conditional sample variance is 0.45 at xi = 0. The conventional MLE parameter estimates imply that this conditional binomial variance should be 0.475, quite close to the actual value. The GEC parameter estimates, on the other hand, imply that the variance should be 0.296, which is much too small. The resulting error is propagated to the standard errors of the coefficients. (See Amato, this volume, for additional discussion of the GEC standard errors.)
2. For nonintegral n, the mean and variance formulas hold only to a very good approximation (see footnote 5), which is sufficient for the expositional purpose at hand.
3. A Comparison of n Estimators for the Binomial Distribution;Olkin;Journal of the American Statistical Association,1981