Abstract
Suppose that we are monitoring incoming observations for a change in mean via a cumulative sum (CUSUM) test statistic. The usual nonparametric methods give first- and second-order approximations for the one- and two-sided cases. Withers and Nadarajah (Statistics and Probability Letters, 79, 2009, 689–697) and Withers and Nadarajah (Statistics and Probability Letters, 79, 2009, 2242–2250) showed how to improve the order of these approximations for linear statistics and for nonlinear statistics with non-zero asymptotic variances. Here, extensions are provided for nonlinear statistics with zero asymptotic variances and for multivariate statistics.
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