STAT7840 1 CH. 5 INFERENCESABOUTA MEAN VECTOR () 1 Inferences about a Mean Vector (n>p) Univariate versions of mean vector inferences. • Hypothesis tests. • Confidence intervals. Inferences about multivariate means (mean vector). • Multivariate hypothesis tests. • Confidence ellipsoids. 2 STAT7840 Introduction/Recurring Themes • Inference - reaching valid conclusions concerning a population on the basis of information obtained from a sample. • Univariate statistics perform inferences for a single variable at a time. • Multivariate statistics perform inferences for a set of variables simultaneously. • A recurring theme of multivariate statistics is that correlated variables (for instance, p of them) should be analyzed jointly. • Hypothesis testing in a multivariate context is more complex than in a univariate setting. • The number of parameters may be staggering. • In a p-variate normal distribution, for example, has The total # of parameters: p means+ p variances+ 2 covariances 【原创】定制代写 r语言/python/spss/matlab/WEKA/sas/sql/C++/stata/eviews 数 据挖掘和统计分析可视化调研报告等服务（附代码数据）,官网咨询链接： ://y0 /teradat STAT7840 3 Motivation for testing p variables multivariately rather than (or in addition to) univariately. There are at least four arguments for a multivariate approach to hypothesis testing: 1) The use of p univariate tests inflates the Type I error rate, α, whereas the multivariate test preserves the exact α level. For example, if we do p = 10 separate univariate tests at the .05 level, the probability of at least one false rejection is greater than .05. If the variables were independent (they rarely are), we would have (under H0) P(at least one rejection) = 1 − P(all 10 tests accept H0) = 1 − (.95)10 = .40. (Not an acceptable error rate!) Motivation for testing p variables multivariately rather than (or in addition to) univariately. 2. The univariate tes
