com.numericalmethod.suanshu.stats.test.regression.linear.heteroskedasticity

Class BreuschPagan

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

com.numericalmethod.suanshu.stats.test.regression.linear.heteroskedasticity.BreuschPagan

All Implemented Interfaces:

java.io.Serializable

public class BreuschPagan
extends HypothesisTest

The Breusch–Pagan test is used to test for heteroskedasticity in a linear regression model. It tests whether the estimated variance of the residuals from a regression are dependent on the values of the independent variables (regressors).

The Breusch–Pagan test tests for conditional heteroskedasticity. The test statistics is computed by regressing squared residuals from the original regression against the original regressors (plus intercept). The test is a chi-squared test: the test statistic distribution is nχ² with k degrees of freedom. If the Breush–Pagan test shows that there is conditional heteroscedasticity, it can be corrected by using the Hansen method, using robust standard errors, or re-thinking the regression equation.

The R equivalent function is bptest.

See Also:

• T. S. Breusch and A. R. Pagan. "A simple test for heteroscedasticity and random coefficient variation," Econometrica 47 (5): 1287–1294, 1979.
• R. Koenker. "A Note on Studentizing a Test for Heteroscedasticity," Journal of Econometrics 17, 107–112. 1981.
• Wikipedia: Breusch–Pagan test

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected int	n number of observations
protected Residuals	residuals

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Constructor Summary

Constructors

Constructor and Description
BreuschPagan(Residuals residuals, boolean studentized) Perform the Breusch-Pagan test to test for heteroskedasticity in a linear regression model.

Method Summary

Modifier and Type	Method and Description
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
protected OLSRegression	getAuxiliaryOLSRegression(Vector y, Residuals residuals) the auxiliary regression
OLSRegression	getAuxiliaryRegression()
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
protected ChiSquareDistribution	getX2()
double	pValue() Get the p-value.
double	statistics() Get the test statistics.

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, oneSidedPvalue

Methods inherited from class java.lang.Object

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

Field Detail

residuals

protected final Residuals residuals

n

protected final int n

number of observations

Constructor Detail

BreuschPagan

public BreuschPagan(Residuals residuals,
                    boolean studentized)

Perform the Breusch-Pagan test to test for heteroskedasticity in a linear regression model.

Parameters:

residuals - the Residuals object from an OLS regression

studentized - true if to use the Koenker's studentized version of the test statistic

Method Detail

getAuxiliaryRegression

public OLSRegression getAuxiliaryRegression()

statistics

public double statistics()

Description copied from class: HypothesisTest

Get the test statistics.

Returns:

the test statistics

See Also:

Wikipedia: Test statistic

getNullHypothesis

public java.lang.String getNullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

getNullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

pValue

public double pValue()

Description copied from class: HypothesisTest

Get the p-value.

Overrides:

pValue in class HypothesisTest

Returns:

the p-value

See Also:

Wikipedia: P-value

getX2

protected ChiSquareDistribution getX2()

getAuxiliaryOLSRegression

protected OLSRegression getAuxiliaryOLSRegression(Vector y,
                                                  Residuals residuals)

the auxiliary regression

Returns:

the auxiliary regression