Accurate tests and intervals based on non-linear cusum statistics

Christopher S. Withers , Saralees Nadarajah

Suppose that we are monitoring incoming observations for a change in mean via a cusum test statistic. The usual nonparametric methods give first and second order approximations for the one- and two-sided cases. Withers and Nadarajah [2009. Statistics and Probability Letters 79 689-697] showed how to improve the order of these approximations for linear statistics. Here, an extension is provided for non-linear statistics with non-zero asymptotic variances. This involves development of two calculi analogous to that of von Mises.

Mots clés: Physical Sciences

Christopher S. Withers, Saralees Nadarajah. Accurate tests and intervals based on non-linear cusum statistics. Statistics and Probability Letters, 2009, 79 (21), pp.2242. ⟨10.1016/j.spl.2009.07.023⟩. ⟨hal-00582595⟩