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A Heteroskedasticity Test Robust to Conditional Mean Misspecification
Byung-Joo Lee
Abstract
This paper proposes a new test statistic to detect the presence of heteroskedasticity. The proposed test does not require a parametric specification of the mean regression function in the first stage regression. The regression function is estimated nonparametrically by the kernel estimation method. The nonparametric residual is estimated and used as a proxy for the random disturbance term. This nonparametric residual is robust to regression function misspecification. Asymptotic normality is established using extensions of classical $U$-statistic theorems. When the disturbance term is heteroskedastic, nonparametric residuals will correctly identify the presence of heteroskedasticity. The test statistic is computed using the nonparametric quantities, but the resulting inference has a standard chi-square distribution.
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