org.drip.spaces.cover

Class L1R1CoveringBounds

java.lang.Object

org.drip.spaces.cover.L1R1CoveringBounds

All Implemented Interfaces:

FunctionClassCoveringBounds

public class L1R1CoveringBounds
extends java.lang.Object
implements FunctionClassCoveringBounds

L1R1CoveringBounds implements the Lower/Upper Bounds for the Class of Non-decreasing R^1 To L1 R^1 Functions that are: - Absolutely Bounded - Have Bounded Variation. The References are: 1) L. Birge (1987): Estimating a Density Under Order Restrictions: Non-asymptotic Minimax Risk, Annals of Statistics 15 995-1012. 2) P. L. Bartlett, S. R. Kulkarni, and S. E. Posner (1997): Covering Numbers for Real-valued Function Classes, IEEE Transactions on Information Theory 43 (5) 1721-1724.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
L1R1CoveringBounds(double dblSupport, double dblVariation, double dblBound) L1R1CoveringBounds Constructor

Method Summary

Modifier and Type	Method and Description
double	bound() Retrieve the Function Bound
double	logLowerBound(double dblCover) Log of the Lower Bound of the Function Covering Number
double	logUpperBound(double dblCover) Log of the Upper Bound of the Function Covering Number
double	support() Retrieve the Ordinate Support
double	variation() Retrieve the Function Variation

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

L1R1CoveringBounds

public L1R1CoveringBounds(double dblSupport,
                          double dblVariation,
                          double dblBound)
                   throws java.lang.Exception

L1R1CoveringBounds Constructor

Parameters:

dblSupport - The Ordinate Support

dblVariation - The Function Variation

dblBound - The Function Bound

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Detail

support

public double support()

Retrieve the Ordinate Support

Returns:

The Ordinate Support

variation

public double variation()

Retrieve the Function Variation

Returns:

The Function Variation

bound

public double bound()

Retrieve the Function Bound

Returns:

The Function Bound

logLowerBound

public double logLowerBound(double dblCover)
                     throws java.lang.Exception

Description copied from interface: FunctionClassCoveringBounds

Log of the Lower Bound of the Function Covering Number

Specified by:

logLowerBound in interface FunctionClassCoveringBounds

Parameters:

dblCover - The Size of the Cover

Returns:

Log of the Lower Bound of the Function Covering Number

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

logUpperBound

public double logUpperBound(double dblCover)
                     throws java.lang.Exception

Description copied from interface: FunctionClassCoveringBounds

Log of the Upper Bound of the Function Covering Number

Specified by:

logUpperBound in interface FunctionClassCoveringBounds

Parameters:

dblCover - The Size of the Cover

Returns:

Log of the Upper Bound of the Function Covering Number

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid