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:
qfloat

M-quantile, must be between 0 and 1

base_normRobustNorm 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

__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

Properties

continuous


Last update: Jul 16, 2024