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[28] [29] Bartlett's test for heteroscedasticity between grouped data, used most commonly in the univariate case, has also been extended for the multivariate case, but a tractable solution only exists for 2 groups. [30] Approximations exist for more than two groups, and they are both called Box's M test.
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.
An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a modification of one of the tests, they can be found to be algebraically equivalent.
In statistics, the Goldfeld–Quandt test checks for heteroscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups, and hence the test is sometimes called a two-group test. The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt. Both a parametric ...
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 ...
Spatial GARCH processes by Otto, Schmid and Garthoff (2018) [15] are considered as the spatial equivalent to the temporal generalized autoregressive conditional heteroscedasticity (GARCH) models. In contrast to the temporal ARCH model, in which the distribution is known given the full information set for the prior periods, the distribution is ...
Hypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests. In multivariate tests the columns of Y are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix.
Notice the relation between the variance and the mean, which implies, for example, heteroscedasticity in a linear model. Therefore, the goal is to find a function g {\displaystyle g} such that Y = g ( X ) {\displaystyle Y=g(X)} has a variance independent (at least approximately) of its expectation.