On sequential detection of parameter changes in linear regression

Horvath et al. [2004. Monitoring changes in linear models. J. Statist. Plann. Inference 126, 225–251] developed a family of monitoring procedures to detect a change in the parameters of a linear regression model. These procedures, which are akin to the schemes proposed by Chu et al. [1996. Monitoring structural change. Econometrica 64, 1045–1065], depend on a parameter 0⩽γ<12. If γγ is close to 12, the detection delay is small, so it is desirable to consider the case γ=12, but an extension is not obvious. We show that it can be developed by establishing a Darling–Erdős type limit theorem.