4.1.2.1.3. statsmodels.base._constraints.transform_params_constraint

statsmodels.base._constraints.transform_params_constraint(params, Sinv, R, q)

find the parameters that statisfy linear constraint from unconstraint

The linear constraint R params = q is imposed.

Parameters:

params : array_like

unconstraint parameters

Sinv : ndarray, 2d, symmetric

covariance matrix of the parameter estimate

R : ndarray, 2d

constraint matrix

q : ndarray, 1d

values of the constraint

Returns:

params_constraint : ndarray

parameters of the same length as params satisfying the constraint

Notes

This is the exact formula for OLS and other linear models. It will be a local approximation for nonlinear models.

TODO: Is Sinv always the covariance matrix? In the linear case it can be (X’X)^{-1} or sigmahat^2 (X’X)^{-1}.

My guess is that this is the point in the subspace that satisfies the constraint that has minimum Mahalanobis distance. Proof ?