  Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often
used to obtain the dependence parameters in copula models from data. It has
been shown that despite being consistent, and in some cases efficient, MPL
estimation can overestimate the level of dependence especially for small weakly
dependent samples. We show that the MPL method uses the expected value of order
statistics and we propose to use instead the median or the mode of the same
order statistics. In a simulation study we compare the finite-sample
performance of the proposed estimators with that of the original MPL and the
inversion method estimators based on Kendall's tau and Spearman's rho. Our
results indicate that the modified MPL estimators, especially the one based on
the mode of the order statistics, have better finite-sample performance, while
still enjoying the large-sample properties of the original MPL method.
