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I've learned that in unconstrained polynomial regression, the optimal order can be determined using two F tests : one to test for the significance of the overall regression, the other to test for the significance of the higher coefficients (assuming the first test passed of course).

However in my application, I'm interested in testing for the appropriateness of a segmented polynomial fit subjected to be first order continuous, with boundary conditions placed at the end of the entire domain as well. The polynomials donothave to have the same order between segments. I should also mention that the join points are known, so I don't have to estimate them.

The closest paper I could find that broaches this topic is Gallant and Fuller's work [1]. Here, they also have a segmented polynomial fit with C1 continuity, but with no constraints. Frustratingly, they make up a test statistic for the appropriateness of their fit "by analogy to linear models theory", yet they provide no references.

I've tried to search for other papers on this topic but to no avail. This leads me to question - is this test statistic trivial to derive for the constrained case, and if so, could you please point me to resources that could help me understand how to do it?

Thanks in advance for your help!

References

[1] Gallant, A.R. and Fuller, W.A. (1973). Fitting segmented polynomial regression models whose join points have to be estimated.J. Amer. Statist. Assoc., 68, 144-147

p.s. If it helps, I'm an engineer who regrettably didn't pay too much attention in his stats course, so any material no matter how trivial it may seem would be appreciated!

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# Appropriateness of Constrained Segmented Univariate Polynomial Regression Model

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