Question

2. Suppose that the data are IID and follow a Mr(μ, Σ) distribution with unknown μ and ,7. Use the Hotelling's Σ. Denote the components of the mean vector as μί, l 1, T2 test to test the following hypotheses at the level 0.05: 0 Versus Ha:A-/s Describe the procedure and your conclusion clearly

**** I am wondering about how to compute my T^2 statistic in this case. Please give me the formula and explicitly state what matrices you use for the linear combination of mu values.***

Answer 1

formula

Hoteling t-square -

For large n, T is approximately chi-square distributed with p degrees of freedom. If we replace the sample variance-covariance matrix, S, by the population variance covariance matrix, Σ

Matrices needed for the linear combination -

$\bar X$ - sample mean matrix of the respective variable

$\mu_0$ - mean matrix of the respective variable to be compared

$\Sigma$ - Sample variance covariance matrix of the variables to be tested

$\Sigma^{-1}$ - Inverse of the sample variance covariance matrix