Maximum pseudo-likelihood estimation in copula models for small weakly dependent samples

TL;DR

This paper proposes modifications to the maximum pseudo-likelihood estimation method for copula models, replacing expected values with median or mode of order statistics to improve small sample dependence estimation accuracy.

Contribution

It introduces a novel approach using median and mode of order statistics in MPL estimation, enhancing finite-sample performance for weakly dependent small samples.

Findings

Mode-based MPL estimator outperforms original MPL in small samples.

Modified estimators maintain large-sample properties.

Simulation results show improved accuracy over traditional methods.

Abstract

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.