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In statistics, the Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser ( fr: Herbert Glejser), regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance. ^[1] After it was found not to be asymptotically valid under asymmetric disturbances, ^[2] similar improvements have been independently suggested by Im, ^[3] and Machado and Santos Silva. ^[4]

Steps for using the Glejser method

Step 1: Estimate original regression with ordinary least squares and find the sample residuals e_i.

Step 2: Regress the absolute value |e_i| on the explanatory variable that is associated with the heteroscedasticity.

${\displaystyle {\begin{aligned}|e_{i}|&=\gamma _{0}+\gamma _{1}X_{i}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\sqrt {X_{i}}}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\frac {1}{X_{i}}}+v_{i}\end{aligned}}}$

Step 3: Select the equation with the highest R² and lowest standard errors to represent heteroscedasticity.

Step 4: Perform a t-test on the equation selected from step 3 on γ₁. If γ₁ is statistically significant, reject the null hypothesis of homoscedasticity.

Software Implementation

Glejser's Test can be implemented in R software using the glejser function of the skedastic package. ^[5] It can also be implemented in SHAZAM econometrics software. ^[6]

See also

Breusch–Pagan test
Goldfeld–Quandt test
Park test
White test

References