ABSTRACT
In univariate inferential statistics, we have discussed point and interval estimation and hypothesis testing concerning single population mean and variance, differences between two population means, and ratio of two population variances. The multivariate counterparts of the above are (i) inference about single population mean vector, (ii) inference about the difference between two population mean vectors, and (iii) inference about covariance and correlation matrices. We will describe them in this chapter. We start with Hotelling’s T2, which is the foundation of multivariate inferential statistics. It is the multivariate counterpart of t-distribution. As we deal with two or more variables simultaneously, the concept of confidence interval (CI) (in univariate statistics) is no longer valid, whose analogue in multivariate domain is confidence region (CR). As it becomes difficult to make decisions based on confidence regions involving more than three variables, simultaneous confidence interval (SCI) for each of the variables needs to be developed. For computation of SCI, both the linear combination and Bonferroni approaches are described in this chapter. Finally, hypothesis testing for mean vectors for both single and two populations is discussed.
