Module estimation 

Available on crate feature estimation only.

Parameter estimation methods for copulas.

This module provides various methods for estimating copula parameters from data:

• Maximum Likelihood Estimation (MLE)
• Inference Functions for Margins (IFM)
• Canonical Maximum Likelihood (CML)
• Method of Moments

Overview

Maximum Likelihood (MLE)

Estimates both marginal and copula parameters jointly by maximizing: L(θ) = Σ log c(F₁(x₁|θ₁), …, Fₐ(xₐ|θₐ)|θ_c)

Inference Functions for Margins (IFM)

Two-stage estimation:

1. Estimate marginal parameters
2. Estimate copula parameters given marginals

Canonical Maximum Likelihood (CML)

Uses empirical CDFs for margins, estimates only copula parameters.

Bibliography

• Joe, H. (2005). Asymptotic efficiency of the two-stage estimation method for copula-based models.
• Genest, C., et al. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions.

Structs

CMLEstimator

Canonical Maximum Likelihood (CML) estimator.

EmpiricalCdf

Empirical CDF estimator.

TauEstimator

Method of moments estimator using Kendall’s tau.

Functions

kendall_tau

Estimate Kendall’s tau from data.

spearman_rho

Estimate Spearman’s rho from data.

to_pseudo_observations

Convert multivariate data to pseudo-observations (uniform margins).