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This is the basis of the Breusch–Pagan test. It is a chi-squared test: the test statistic is distributed nχ 2 with k degrees of freedom. If the test statistic has a p-value below an appropriate threshold (e.g. p < 0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed.
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these.
He is noted for the Breusch–Pagan test from the paper (with Adrian Pagan) "A simple test for heteroscedasticity and random coefficient variation" (see Noted works, below). Another contribution to econometrics is the serial correlation Lagrange multiplier test, often called Breusch–Godfrey test after Breusch and Leslie G. Godfrey , which can ...
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
Student's t test for testing inclusion of a single explanatory variable, or the F test for testing inclusion of a group of variables, both under the assumption that model errors are homoscedastic and have a normal distribution. Change of model structure between groups of observations. Structural break test. Chow test; Comparing model structures
Pagan is known for work in time-series econometrics and hypothesis testing, notably including the Breusch–Pagan test for heteroscedasticity and other applications of the Lagrange multiplier test. His recent work has focused on macro-econometric modeling and its uses in policy analysis and for the explanation of business cycles.
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