statsmodels.regression.dimred.SlicedInverseReg.fit_regularized

SlicedInverseReg.fit_regularized(ndim=1, pen_mat=None, slice_n=20, maxiter=100, gtol=0.001, **kwargs)

Estimate the EDR space using regularized SIR.

Parameters

ndim: int

The number of EDR directions to estimate

pen_matarray_like

A 2d array such that the squared Frobenius norm of dot(pen_mat, dirs)` is added to the objective function, where dirs is an orthogonal array whose columns span the estimated EDR space.

slice_nint, optional

Target number of observations per slice

maxiter :int

The maximum number of iterations for estimating the EDR space.

gtol :float

If the norm of the gradient of the objective function falls below this value, the algorithm has converged.

Returns

A results class instance.

Notes

If each row of exog can be viewed as containing the values of a function evaluated at equally-spaced locations, then setting the rows of pen_mat to [[1, -2, 1, …], [0, 1, -2, 1, ..], …] will give smooth EDR coefficients. This is a form of “functional SIR” using the squared second derivative as a penalty.

References

L. Ferre, A.F. Yao (2003). Functional sliced inverse regression analysis. Statistics: a journal of theoretical and applied statistics 37(6) 475-488.