Mean Vectors and Covariance Matrices
Mean Vectors and Covariance Matrices
Mean Vectors and Covariance Matrices
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The Exponent Term<br />
• The term in the exponent (without the − 1 ) is called the squared<br />
2<br />
Mahalanobis Distance<br />
d 2 x p = x T p − μ T Σ −1 x T p − μ<br />
‣ Sometimes called the statistical distance<br />
‣ Describes how far an observation is from its mean vector, in<br />
st<strong>and</strong>ardized units<br />
‣ Like a multivariate Z score (but, if data are MVN, is actually distributed as a<br />
χ 2 variable with DF = number of variables in X)<br />
‣ Can be used to assess if data follow MVN<br />
PSYC 943: Lecture 11 38
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