The sample scatter matrix (or mean-corrected sum of squares and cross products [SSCP] matrix) $S$ of multivariate normally distributed vectors $\boldsymbol x_{j}$ ($j=1,\ldots,n)$ each of size $m$ (e.g., https://en.wikipedia.org/wiki/Scatter_matrix) has a Wishart distribution:

$S\sim \mathcal{W}_m(\Sigma,n-1)$

with $(n-1)$ degrees of freedom and scale matrix $\Sigma$ (e.g., Pham-Gia & Choulakian, 2014, p. 331).

What is the distribution of $S$ (and how can $S$ be calculated) if the vectors $\boldsymbol x_{j}$ contain missing values (under the assumption that the values are missing completely at random, MCAR)?


Pham-Gia, T., & Choulakian, V. (2014). Distribution of the sample correlation matrix and applications. Open Journal of Statistics, 4, 330–344. http://www.dx.doi.org/10.4236/ojs.2014.45033


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