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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 ...
This test, and an estimator for heteroscedasticity-consistent standard errors, were proposed by Halbert White in 1980. [1] These methods have become widely used, making this paper one of the most cited articles in economics. [2]
Equivalently, heteroscedasticity refers to unequal conditional variances in the response variables , such that (|) =, again a value that ...
While the OLS point estimator remains unbiased, it is not "best" in the sense of having minimum mean square error, and the OLS variance estimator ^ [^] does not provide a consistent estimate of the variance of the OLS estimates.
A parametric test for equal variance can be visualized by indexing the data by some variable, removing data points in the center and comparing the mean deviations of the left and right side. In statistics, the Goldfeld–Quandt test checks for heteroscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups ...
Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.
Heteroscedasticity, second-order statistical misspecification; Information matrix test; Model identification; Principle of Parsimony; Spurious relationship; Statistical conclusion validity; Statistical inference; Statistical learning theory