Multivariate Autoregressive Techniques for Constructing Confidence Regions on the Mean Vector
提出一种基于向量自回归模型的均值向量置信域构建方法，通过实验比较发现该方法在体积上优于其他方法，适用于大样本且存在向量自回归依赖结构的数据。
We develop a method for constructing confidence regions on the mean vectors of multivariate processes that is based on a vector autoregressive (VAR) representation of the data-generating process. A confidence-region-construction algorithm for a general autoregressive model is given. We establish the asymptotic validity of the confidence-region estimator (that is, the exact achievement of nominal coverage probability as the sample size tends to infinity) when the output process is a stationary vector autoregressive process of known, finite order. With respect to confidence-region volume, coverage probability, and execution time, we carry out an experimental performance comparison of VAR versus the methods of Bonferroni Batch Means (BBM), Multivariate Batch Means (MBM), and Multivariate Spectral Analysis (SPA). The experimental results indicate that (i) VAR delivered confidence regions with the smallest volume; (ii) BBM delivered confidence regions with the largest volume, the highest coverage and the smallest execution time; (iii) in small samples, all of the methods might yield confidence-region estimators whose coverage differs significantly from the nominal level; and (iv) in large samples for which the sample autocorrelation function indicates a vector autoregressive dependence structure, VAR is a viable technique for simulation output analysis.