Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Covariance ▷ Sample covariance

Definition: Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ and $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ be samples from random variables $X$ and $Y$. Then, the sample covariance of $x$ and $y$ is given by

\[\label{eq:cov-samp} \hat{\sigma}_{xy} = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x}) (y_i - \bar{y})\]

and the unbiased sample covariance of $x$ and $y$ is given by

\[\label{eq:cov-samp-unb} s_{xy} = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}) (y_i - \bar{y})\]

where $\bar{x}$ and $\bar{y}$ are the sample means.

 
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Metadata: ID: D144 | shortcut: cov-samp | author: ciaranmci | date: 2021-04-21, 06:53.