pub fn flm_f_test(fit: &FregreLmResult) -> Result<TestResult, FdarError>Expand description
Overall-significance F-test for a fitted functional linear model.
Tests the null hypothesis H0 that the functional coefficient has no effect — i.e. the FLM reduces to an intercept-only model. The statistic is the classical regression F built from the model R²:
F = (R² / p) / ((1 − R²) / (n − p − 1))where p = fit.ncomp is the number of effective FPC parameters and
n = fit.residuals.len() is the sample size. Under H0, F follows an
F(p, n − p − 1) distribution, so the p-value is the F upper-tail
(survival) probability of the observed statistic. A small p-value rejects
H0 in favour of a genuine functional effect.
Returns a TestResult with n_perm = 0 (this is an asymptotic /
closed-form test, not a permutation test).
§Errors
Returns FdarError::InvalidParameter when the fit is degenerate: ncomp
is zero, the denominator degrees of freedom n − p − 1 are non-positive,
or r_squared is not finite or is >= 1.0 (a perfect fit makes the F
statistic ill-defined).