Bootstrapped White’s test for heteroskedasticity in regression models

A Simulation Study of White's Test for Heteroskedasticity in Fixed and Stochastic Regression Models

“…We remark the bootstrap method of Jeong and Lee (1999) results in the same bootstrapped distribution of White's test as a standard bootstrap procedure in the linear regression model if there exists an intercept in the model (cf., Ando and Hodoshima, 2007). In a related study of Hodoshima and Ando (2007), we presented a simulation study to compare White's test for heteroskedasticity and tests based on several bootstrap procedures, i.e., a standard bootstrap procedure or the method of Jeong and Lee (1999), a bootstrap due to Wu (1986), a so-called pairwise bootstrap due to Freedman (1981) and Efron (1982) and its modification, two wild bootstrap methods due to Mammen (1993) and Davidson and Flachaire (2001) and their modifications, to investigate how they perform in the stochastic regression model under the joint null hypothesis of homoskedasticity and independence of explanatory variables and error term and its three alternative hypotheses, i.e., (i) heteroskedasticity and independence, (ii) homoskedasticity and non independence, and (iii) heteroskedasticity and non independence.…”

“…It can be used in fixed regression models where explanatory variables are fixed and also in stochastic regression models where explanatory variables are random and not given (cf., p. 818 of White, 1980). A recent study by Jeong and Lee (1999) proposed a bootstrap procedure to improve the finite-sample properties of White's test under homoskedasticity as well as heteroskedasticity. The bootstrap method was demonstrated in Jeong and Lee (1999) to work better in small samples than a method of White where the underlying simulation setup was a fixed regression model with a symmetric error term.…”

“…A recent study by Jeong and Lee (1999) proposed a bootstrap procedure to improve the finite-sample properties of White's test under homoskedasticity as well as heteroskedasticity. The bootstrap method was demonstrated in Jeong and Lee (1999) to work better in small samples than a method of White where the underlying simulation setup was a fixed regression model with a symmetric error term. Although the difference of fixed and stochastic regression models can make a large difference in the inference, no comparison of fixed and stochastic regression models was provided in the literature with respect to the small-sample performance of White's test.…”

“…In a related study of Hodoshima and Ando (2007), we presented a simulation study to compare White's test for heteroskedasticity and tests based on several bootstrap procedures, i.e., a standard bootstrap procedure or the method of Jeong and Lee (1999), a bootstrap due to Wu (1986), a so-called pairwise bootstrap due to Freedman (1981) and Efron (1982) and its modification, two wild bootstrap methods due to Mammen (1993) and Davidson and Flachaire (2001) and their modifications, to investigate how they perform in the stochastic regression model under the joint null hypothesis of homoskedasticity and independence of explanatory variables and error term and its three alternative hypotheses, i.e., (i) heteroskedasticity and independence, (ii) homoskedasticity and non independence, and (iii) heteroskedasticity and non independence. A standard bootstrap or the method of Jeong and Lee (1999) was found in Hodoshima and Ando (2007) to work best in the stochastic regression model. However, we did not make any comparison between fixed and stochastic regression models in Hodoshima and Ando (2007).…”

“…However, we did not make any comparison between fixed and stochastic regression models in Hodoshima and Ando (2007). The models of Jeong and Lee (1999) and Hodoshima and Ando (2007) are very different. Therefore, currently it is not clear in the existing literature how White's test and bootstrap tests perform in fixed (stochastic) regression models as compared to in stochastic (fixed) regression models.…”