Correlation and the Performance of One-Sided Cumulative Sum Tests.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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The purpose of this note is to first show how the theory of weak convergence of cumulative sums to the Wiener Process can be employed to obtain a large sample approximation to the one-sided cu-sum test proposed by Page 1955. This approximation seems to be quite accurate even for moderate sample sizes. Secondly, the authors employ the general theory to study the effect of correlation among the observations on the level and critical values. Particular attention is placed on the first order moving average and autoregressive models. In order to treat the sequential version of the test, we employ the same Wiener process approximation to study changes caused in average run length, under the null hypothesis, by the correlation structure. Author
- Statistics and Probability