- class statsmodels.robust.norms.MQuantileNorm(q, base_norm)¶
M-quantiles objective function based on a base norm
This norm has the same asymmetric structure as the objective function in QuantileRegression but replaces the L1 absolute value by a chosen base norm.
rho_q(u) = abs(q - I(q < 0)) * rho_base(u)
rho_q(u) = q * rho_base(u) if u >= 0 rho_q(u) = (1 - q) * rho_base(u) if u < 0
This is mainly for base norms that are not redescending, like HuberT or LeastSquares. (See Jones for the relationship of M-quantiles to quantiles in the case of non-redescending Norms.)
Expectiles are M-quantiles with the LeastSquares as base norm.
Returns the value of estimator rho applied to an input
The psi function for MQuantileNorm estimator.
The derivative of MQuantileNorm function
The robust criterion function for MQuantileNorm.
MQuantileNorm weighting function for the IRLS algorithm