ENH: estimation subject to nonlinear constraints, e.g. in GLM
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Assessment
- Difficulty
- 5/5
- Estimated time
- Over a week
- Newbie friendliness
- 25/100
Research direction
Start by reading the current fit_constrained implementation and the GLM estimation code it supports. Clarify how nonlinear constraints for predicted values or probabilities should be represented, then identify the relevant estimation tests and define coverage for constrained profile and score confidence intervals.
Written by the indexing model from the issue text.
Description
just a use case idea:
profile and score confidence intervals for parameters need constrained estimation. In GLM the constraints are linear.
If we want the analogous profile and score confidence interval on the predicted values, e.g. probabilities in Binomial, then we would need a nonlinear constraint that prob takes on a specific value.
(On second thought:) It might be possible to transform this to a constraint on a linear combination of parameters in some cases with single-index or link function, by getting the equivalent constraints on the linear predictor.
The current fit_constrained only allows linear/affine constraints on params that are coefficients for exog.
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