statsmodels.robust.norms.MQuantileNorm¶

class statsmodels.robust.norms.MQuantileNorm(q, base_norm)[source]¶

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)

or, equivalently,

rho_q(u) = q * rho_base(u) if u >= 0 rho_q(u) = (1 - q) * rho_base(u) if u < 0

Parameters:¶

q : float¶

M-quantile, must be between 0 and 1

base_norm : RobustNorm instance¶

basic norm that is transformed into an asymmetric M-quantile norm

Notes

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.

References

Methods

psi(z)	The psi function for MQuantileNorm estimator.
psi_deriv(z)	The derivative of MQuantileNorm function
rho(z)	The robust criterion function for MQuantileNorm.
weights(z)	MQuantileNorm weighting function for the IRLS algorithm