You tube channels for Learning

TileStats - YouTube

StatQuest with Josh Starmer - YouTube

Matthew E. Clapham - YouTube

Joshua Emmanuel - YouTube 

Probability Course - YouTube check on probabilitycourse.com

Dr Nic's Maths and Stats - YouTube 

WikiofScience JKAI - YouTube

Probability Course - YouTube


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Robust covariance matrix estimation in SPSS

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Clear Understanding on Mahalanobis Distance

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  Clear Understanding on Mahalanobis Distance In multivariate/ multicharacteristics data, a measure of divergence or distance between groups in terms of  multiple characteristics is required. Lets consider, you are interested in measuring the difference (distance) between groups G1 and G2 (each of p-dimensional). A common assumption is to take the p-dimensional random vector X  , from each group, as having same variation about its mean within either group. The difference between the groups can be considered in terms of difference between mean vectors of X, in each group relative to the common within-group variation  (using common (pooled) covariance matrix). The most often used measure for multiple characteristics data is, Mahalanobis distance (Mahalanobis  Δ , where  Δ  is Uppercase Delta). The square of Mahalanobis distance is given by,  Δ 2 =  (µ 1 -µ 2 ) T Σ -1 (µ 1 -µ 2 ) or          Δ 2 =  (µ 1 -µ 2 ) ′ ...
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Vignettes for Matrix concepts, related operations

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