fdars.tolerance

Tolerance bands, confidence bands, and equivalence testing for functional data.

Functions

Function	Description
fpca_tolerance_band	FPCA-based simultaneous tolerance band
conformal_prediction_band	Conformal prediction band
scb_mean_degras	Simultaneous confidence band for the mean (Degras)
equivalence_test	Functional equivalence test (TOST)

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fpca_tolerance_band

fdars.fpca_tolerance_band(data, ncomp=3, nb=1000, coverage=0.95, seed=42)

FPCA-based simultaneous tolerance band via bootstrap.

Parameter	Type	Default	Description
data	ndarray (n, m)		Functional data
ncomp	int	3	Number of FPC components
nb	int	1000	Number of bootstrap replicates
coverage	float	0.95	Coverage level
seed	int	42	Random seed

Returns	Type	Description
result	dict	Keys: upper (m,), lower (m,), center (m,), half_width (m,)

band = fdars.fpca_tolerance_band(data, ncomp=3, coverage=0.95)

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conformal_prediction_band

fdars.conformal_prediction_band(data, coverage=0.95, cal_fraction=0.25, seed=42)

Distribution-free conformal prediction band.

Parameter	Type	Default	Description
data	ndarray (n, m)		Functional data
coverage	float	0.95	Target coverage level
cal_fraction	float	0.25	Fraction used for calibration
seed	int	42	Random seed

Returns	Type	Description
result	dict	Keys: upper (m,), lower (m,), center (m,), half_width (m,)

band = fdars.conformal_prediction_band(data, coverage=0.90)

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scb_mean_degras

fdars.scb_mean_degras(data, argvals, bandwidth=0.0, nb=1000, confidence=0.95)

Simultaneous confidence band for the mean function using the Degras (2011) multiplier bootstrap method.

Parameter	Type	Default	Description
data	ndarray (n, m)		Functional data
argvals	ndarray (m,)		Evaluation points
bandwidth	float	0.0	Kernel smoothing bandwidth; 0.0 for auto
nb	int	1000	Number of bootstrap samples
confidence	float	0.95	Confidence level

Returns	Type	Description
result	dict	Keys: upper (m,), lower (m,), center (m,), half_width (m,)

t = np.linspace(0, 1, 100)
scb = fdars.scb_mean_degras(data, t, confidence=0.95)

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equivalence_test

fdars.equivalence_test(data1, data2, delta, alpha=0.05, nb=1000, seed=42)

Functional equivalence test (TOST procedure). Tests whether two groups of curves are equivalent within a margin delta.

Parameter	Type	Default	Description
data1	ndarray (n1, m)		First group
data2	ndarray (n2, m)		Second group
delta	float		Equivalence margin
alpha	float	0.05	Significance level
nb	int	1000	Number of bootstrap replicates
seed	int	42	Random seed

Returns	Type	Description
result	dict	Keys: equivalent (bool), p_value, test_statistic

result = fdars.equivalence_test(group1, group2, delta=0.5, alpha=0.05)
if result["equivalent"]:
    print(f"Groups are equivalent (p={result['p_value']:.4f})")