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
- q
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
__call__
(z)Returns the value of estimator rho applied to an input
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