The sample covariance matrix is a generalization of a formula for the variance of a sample of

Question:

The sample covariance matrix is a generalization of a formula for the variance of a sample of N scalar measurements, say, t1...........tN . If m is the average of t1...........tN , then the sample variance is given by


image


Show how the sample covariance matrix, S, defined prior to Example 3, may be written in a form similar to (1). Use partitioned matrix multiplication to write S as 1/(N – 1) times the sum of N matrices of size p x p. For 1 ≤ k ≤ N, write Xk – M in place of  X̂k.



Example 3


image

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

Question Posted: