Читать книгу Data Science in Theory and Practice - Maria Cristina Mariani - Страница 34

The sample variance of can be found as the sample variance of or directly from and , where is the sample covariance matrix of :

(3.13)

We recall from Section 2.3 that variance is always nonnegative. Thus, we have , and therefore, , for every .

If we define another linear combination , where is a vector of constants different from , then the sample covariance of and is given by

(3.14)

where is the number of measurements.

Please refer to Johnson and Wichern (2014) for the proof of (3.14).