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

Methods

__call__(z)

Returns the value of estimator rho applied to an input

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