Testing regression coefficients when error terms are not independently and identically distributed

The authors consider the problem of testing a linear hypothesis on some regression coefficients in a linear regression model. When they misspecify the regression error covariance matrix and test the null hypothesis by an F-test, the significance level will be affected. If the misspecification is small, they might fail to detect the misspecification, but the effect on the significance level could be serious. The authors derive valid expansions on the distribution function of an F-test statistic under misspecified regression error covariance matrices. Based on the expansions, they present simple, useful, and fairly exact approximations to them in the cases of AR(1) errors and heteroscedasticity. Some simulation results are also given. [In Japanese.]