# Multivariate Analysis-Distribution of Hotelling T2 Statistic (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 1 of 1

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## Question number: 1

» Multivariate Analysis » Distribution of Hotelling T2 Statistic » Use for Testing

Appeared in Year: 2015

### Describe in Detail

Show that T ^{2} statistic is invariant under changes in the unit of measurements for a p×1 random vector X of the form __Y__ =C __X __ + __d __ where C is a p×p nonsingular matrix, __d__ is a p×1 vector.

### Explanation

T ^{2} statistic can be computed from __X__. Here we have to compute it form __Y__ and both will be same. Here

Let , then and

So, T ^{2} -statistic comes into existence for testing hypothesis of the form

Since is known vector,

If we have a setup

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