fdars.outliers¶

Outlier detection methods for functional data.

Functions¶

Function	Description
`detect_outliers_lrt`	LRT-based outlier detection with bootstrap
`outliergram`	Outliergram (MEI vs MBD)
`magnitude_shape`	Magnitude-shape outlyingness

fdars.detect_outliers_lrt(data, alpha=0.05, n_bootstrap=200, trim=0.1, smo=0.02)

Likelihood ratio test for outlier detection with bootstrap calibration.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional data
`alpha`	`float`	`0.05`	Significance level
`n_bootstrap`	`int`	`200`	Number of bootstrap samples
`trim`	`float`	`0.1`	Trimming proportion
`smo`	`float`	`0.02`	Smoothing parameter

Returns	Type	Description
result	`dict`	Keys: `outliers` (bool array of length n), `threshold`

result = fdars.detect_outliers_lrt(data, alpha=0.05)
outlier_idx = np.where(result["outliers"])[0]

fdars.outliergram(data, factor=1.5)

Outliergram method. Computes Modified Epigraph Index (MEI) and Modified Band Depth (MBD), then flags outliers based on a parabolic rule.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional data
`factor`	`float`	`1.5`	Outlier detection factor

Returns	Type	Description
result	`dict`	Keys: `mei` (n,), `mbd` (n,), `outliers` (bool array of length n)

result = fdars.outliergram(data, factor=1.5)

fdars.magnitude_shape(data)

Compute magnitude and shape outlyingness measures. Magnitude captures vertical outliers; shape captures curves with unusual patterns.

Parameter	Type	Description
`data`	`ndarray (n, m)`	Functional data

Returns	Type	Description
result	`dict`	Keys: `magnitude` (n,), `shape` (n,)

result = fdars.magnitude_shape(data)
# Flag observations with extreme magnitude or shape
outliers = (result["magnitude"] > 3) | (result["shape"] > 3)