Huber M-estimation (CCF for EAD):

 Huber M-estimation is a robust regression technique used to address the influence of outliers on model parameters. It is used to calculate CCF (Credit Conversion Factor) models for EAD (Exposure at Default).

Huber M-estimation ensures robust parameter estimation by minimizing the impact of extreme observations (e.g., outliers in utilization rates, credit line drawdowns, or other key drivers).

Huber M-estimation uses a loss function (1) that transitions from squared error to absolute error depending on a threshold 𝛿:
δ based on the expected distribution of residuals.

e.g. δ=m * Stdev of errors
- If ∣ri∣≤m * Stdev, weight wi=1

- If ∣ri∣>m * Stdev the weight wi= m * Stdev / ∣ri∣


Steps:
Y (CCF) =β0​+ β1​X+ ϵ,
fit the Ordinary Least Squares (OLS) regression:
β^​=(X^TX)^−1 * X^TY
residuals ri=yi−y^i

Define the Huber loss function (1) to calculate weights.

Using weights, modify the regression:
β^​=(X^T*W*X)^−1X^T*W*Y