KernelDensityOptions.CrossValidated Method

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

Definition

Namespace: Numerics.NET.Statistics
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.9.0

public static KernelDensityOptions CrossValidated(
	double minimumBandwidth,
	double maximumBandwidth,
	double bandwidthAdjustment = 1
)

Visual Basic

Public Shared Function CrossValidated ( 
	minimumBandwidth As Double,
	maximumBandwidth As Double,
	Optional bandwidthAdjustment As Double = 1
) As KernelDensityOptions

C++/CLI

public:
static KernelDensityOptions^ CrossValidated(
	double minimumBandwidth, 
	double maximumBandwidth, 
	double bandwidthAdjustment = 1
)

static member CrossValidated : 
        minimumBandwidth : float * 
        maximumBandwidth : float * 
        ?bandwidthAdjustment : float 
(* Defaults:
        let _bandwidthAdjustment = defaultArg bandwidthAdjustment 1
*)
-> KernelDensityOptions

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

ArgumentOutOfRangeException

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