Abstract In this article Wald’s sequential probability ratio test (SPRT) is implemented for multivariate normal distribution, for independent and autocorrelated data and known covariance matrix. The methodology based on residuals from the vector autoregressive moving average (VARMA) class models is presented for autocorrelated data. In this approach the average sample size required to take a decision in the sequential test is based on the Mahalanobis distance between the vectors of the intercept constants with respect to the error covariance matrix. Monte Carlo simulations were performed considering different scenarios for bivariate normal distribution. For fixed probabilities of type I and II errors, the results showed that the estimated average sample sizes to stop the sequential test were a little larger than those expected by Wald’s theory for autocorrelated and independent data. Under independence assumption the SPRT estimated sample sizes were also smaller than the sample sizes required by Hotelling’s test. It was shown that the omission of the correlation structure of the data strongly affects the type I and II errors of the sequential test. An example in the quality control field is presented using real data from a pig iron production process and the multivariate VAR(1) model.

中文翻译：

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关于多元正态分布和相关数据下向量均值的 Wald 序列检验

摘要 在本文中，对多元正态分布、独立和自相关数据以及已知协方差矩阵实施了 Wald 序列概率比检验 (SPRT)。针对自相关数据提出了基于矢量自回归移动平均 (VARMA) 类模型残差的方法。在这种方法中，在顺序测试中做出决定所需的平均样本大小基于截距常数的向量与误差协方差矩阵之间的马氏距离。考虑到二元正态分布的不同场景，进行了蒙特卡罗模拟。对于 I 类和 II 类错误的固定概率，结果表明，停止顺序检验的估计平均样本量略大于 Wald 理论对自相关和独立数据的预期。在独立性假设下，SPRT 估计的样本量也小于 Hotelling 检验所需的样本量。结果表明，数据相关结构的遗漏对顺序检验的 I 类和 II 类错误有很大影响。使用来自生铁生产过程的真实数据和多元 VAR(1) 模型展示了质量控制领域的一个示例。结果表明，数据相关结构的遗漏对顺序检验的 I 类和 II 类错误有很大影响。使用来自生铁生产过程的真实数据和多元 VAR(1) 模型展示了质量控制领域的一个示例。结果表明，数据相关结构的遗漏对顺序检验的 I 类和 II 类错误有很大影响。使用来自生铁生产过程的真实数据和多元 VAR(1) 模型展示了质量控制领域的一个示例。