Estimating Copula Dependence for Discrete Poisson Variables

Summary

The document poses a statistical estimation problem involving 30 discrete random variables, each assumed to follow a Poisson distribution, with dependence represented by a copula. The author seeks to estimate the copula parameter from observed data and reports that direct maximum likelihood is too computationally costly in this discrete setting.

No answer, estimator, approximation, or computational strategy is included, so the text does not establish how the problem should be solved or whether a particular copula is appropriate. Its value is in identifying a practical challenge: discrete margins complicate likelihood-based copula estimation and can make computation expensive. It gives no data description, dependence structure, benchmark, or results to assess. A researcher using this setup would need to investigate suitable discrete-copula estimation methods and evaluate their assumptions and computational performance separately.

Key ideas

• The problem concerns dependence estimation across 30 Poisson-distributed discrete variables.
• The author proposes a copula to represent dependence among the variables.
• Direct maximum likelihood is reported to require too much computation for the stated problem.
• The document contains no proposed alternative estimator or empirical results.

Tags

# Estimation of copula for discrete random variable


# Estimation of copula for discrete random variable












I'm interested in the estimation of parameter of copula for discrete random variables.

The problem is described as follow: I have 30 discrete random variables $X_1,.., X_{30}$, each random variable is Poisson distributed, and I assume that they correlates by a copula. Now i want to estimate the parameter of that copula base on the data of these 30 random variables.

Could you please tell me which method to be use ? For now, the maximum likelihood estimation fails because it requires a lot of computing time in the case of discrete random variable.

Thank you very much for your help!

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