Accurate Tests and Intervals Based on Multivariate CUSUM Statistics

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.

Keywords:

• Approximations
• CUSUM
• Multivariate statistics

Subject Classifications:

• 62L10
• 62L12

ACKNOWLEDGMENT

The authors thank the Editor-in-Chief for careful reading and for his comments, which greatly improved the article.

Notes

Recommended by N. Mukhopadhyay.