dev.nm.stat.random.variancereduction

Class ControlVariates

java.lang.Object

dev.nm.stat.random.variancereduction.ControlVariates

All Implemented Interfaces:

MeanEstimator

public class ControlVariates
extends Object
implements MeanEstimator

Control variates method is a variance reduction technique that exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity. We estimate the mean of \(f_i(x;b) = f_i(x) - b(g_i(x) - E(g))\).

See Also:

• "Wikipedia: Control variates"
• Glasserman, Paul. "Chapter 4.1. Control Variates," Monte Carlo Methods in Financial Engineering. 2003

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	ControlVariates.Estimator

Constructor Summary

Constructors

Constructor and Description
ControlVariates(UnivariateRealFunction f, UnivariateRealFunction g, double Eg, double b, RandomNumberGenerator X) Estimates \(E(f(X_1))\), where f is a function of a random variable.

Method Summary

Modifier and Type	Method and Description
double	cov()
ControlVariates.Estimator	estimate(int n) Gets an estimator.

Methods inherited from class java.lang.Object

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

Constructor Detail

ControlVariates

public ControlVariates(UnivariateRealFunction f,
                       UnivariateRealFunction g,
                       double Eg,
                       double b,
                       RandomNumberGenerator X)

Estimates \(E(f(X_1))\), where f is a function of a random variable.

Parameters:

f - the random function to evaluate the expectation of

g - the random function with known value

Eg - the expectation of g

b - a coefficient

X - a random number generator

Method Detail

cov

public double cov()

estimate

public ControlVariates.Estimator estimate(int n)

Description copied from interface: MeanEstimator

Gets an estimator.

Specified by:

estimate in interface MeanEstimator

Parameters:

n - the number of samples to draw for the estimation

Returns:

an estimator