Chow and Wald Tests for Parameter Equality under Conditions of Heteroskedasticety
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초록
본 논문은 그룹된 자료에서 각 그룹내에 이분성(within-group heteroskedasticity)이 존재할 때 다중선형 회귀방정식 상의 파라미터 동질성 검사(tests for equality of parameters)를 위해 Chow test와 EWLS(Least squares estimators using estimated weights)-based and OLS/HCCME(Heteroskedasticity Consistent Covariance Matrix Estimators)-based Wald tests를 실시하였다. 먼저 Chow test에서는 우리가 생각하는 F-분포도와는 심각할 정도로 다르게 양방향으로 차이가 나타났다. 그리고 Wald test 역시, 특히 표본수가 적을 경우 상당한 양의 편의(bias) 현상을 발견 할 수 있었다. 이러한 현상을 개선 또는 교정하기 위하여 본 논문에서는 다양한 표본을 생성한 후, bootstrap 방법을 이용하여 가장 좋은 방법을 도출하려 시도하였다. 여러 가지 방법 중 EWLS- based Wald test 방법이 만족할 정도의 가장 좋은 결과를 거둘 수 있었다. 따라서 이분성이 존재하고 특히 표본수가 적은 자료를 이용하여 파라미터 동질성 검사를 실시할 경우, EWLS-based Wald test를 이용하면 만족한 결과를 얻을 것으로 판단된다.
Abstract
This paper considers both the Chow and the EWLS-based and OLS/HCCME-based Wald tests for equality of parameters in linear regression across different samples under conditions of within-group heteroskedasticity. The Chow test is often severely biased compared to its presumed Fdistribution, both upward and downward. The Wald test also shows surprising amounts of "small sample" bias, even in relatively large samples. This paper proposes a bootstrap procedure that works quite satisfactorily and indicates that, even if the variance function is misspecified, the EWLS-based Wald test is generally preferred.
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