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An alternative to explicitly modelling the heteroskedasticity is using a resampling method such as the wild bootstrap. Given that the studentized bootstrap, which standardizes the resampled statistic by its standard error, yields an asymptotic refinement, [13] heteroskedasticity-robust standard errors remain nevertheless useful.
Step 3: Select the equation with the highest R 2 and lowest standard errors to represent heteroscedasticity. Step 4: Perform a t-test on the equation selected from step 3 on γ 1. If γ 1 is statistically significant, reject the null hypothesis of homoscedasticity.
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. If the Breusch–Pagan test shows that there is conditional heteroskedasticity, one could either use weighted least squares (if the source of heteroskedasticity is known) or ...
Heteroscedasticity often occurs when there is a large difference among the sizes of the observations. A classic example of heteroscedasticity is that of income versus expenditure on meals. A wealthy person may eat inexpensive food sometimes and expensive food at other times. A poor person will almost always eat inexpensive food.
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics , a sequence of random variables is homoscedastic ( / ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k / ) if all its random variables have the same finite variance ; this is also known as homogeneity of variance.
Heteroscedasticity, second-order statistical misspecification; Information matrix test; Model identification; Principle of Parsimony; Spurious relationship; Statistical conclusion validity; Statistical inference; Statistical learning theory
Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test. His results show limited success for the Goldfeld–Quandt test except under cases of "pure heteroskedasticity"—where variance can be described as a function of only the underlying explanatory variable.
Heteroscedasticity allows the variance to be dependent on x, which is more accurate for many real scenarios. For example, the variance of expenditure is often larger for individuals with higher income than for individuals with lower incomes.