KernelDensityOptions.CrossValidated Method

Creates Gaussian least-squares cross-validation options with explicit bandwidth bounds.

Definition

Namespace: Numerics.NET.Statistics.KernelDensityEstimation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.9.0
C# 
public static KernelDensityOptions CrossValidated(
	double minimumBandwidth,
	double maximumBandwidth,
	double bandwidthAdjustment = 1
)

Parameters

minimumBandwidth  Double
The finite positive lower bound, in fitting-coordinate units before adjustment.
maximumBandwidth  Double
The finite positive upper bound in fitting-coordinate units, strictly above the lower bound, before adjustment.
bandwidthAdjustment  Double  (Optional)
A finite positive multiplier applied after selection. The default is 1.

Return Value

KernelDensityOptions
Immutable options for bounded Gaussian cross-validation.

Remarks

Minimizes integrated squared density minus twice the weighted leave-one-out density. Each held-out observation's remaining relative masses are renormalized. A deterministic logarithmic scan with local refinement returns the best evaluated width; it does not guarantee a global minimum. Quadratic pair sums make this suitable for moderate samples. Duplicate-heavy data may favor the lower bound. Inspect the fitted estimate's boundary status before accepting such a result.

Exceptions

ArgumentOutOfRangeExceptionA bound or adjustment is not finite and positive, or the bounds are not strictly ordered.

See Also