Minimum generalized variance for outlier detection I'm currently reading the paper Distribution of Variables by Method of Outlier Detection and am trying to understand the section on Minimum generalized variance
If my understanding is roughly correct, it basically starts off with no points and then adds points to a data-set. Each point is then assign a variance score. The further away the data point is from the median the more variance it accrues. The paper does a much better job at explaining it and is very accessible. My question is concerned with the section on cutoffs. For multi-variate outliers it uses the formula
$M_{G}+\sqrt{\chi_{0.975 . p}^{2}}\left(q_{3}-q_{1}\right)$
I understand the role of q1 and q2 but could anyone explain to me what the $\chi_{0.975 . p}^{2}$ in the section of the formula represents?
 A: Comment:  Short answer: I don't really know. Explorations follow.
In the linked paper, it seems early on that $p$ is degrees
of freedom (or observations or dimensions). Then just after display (6) the author
seems about to define $\chi_{0.975,p}^2$ when the sentence
ends abruptly. At (7) this expression occurs again.
My guess is that this is the value that cuts probability 0.025 from
the upper tail of $\mathsf{Chisq}(\nu = p).$ Taking $p=2$ in (7)
this would lead to $\sqrt{\chi_{0.975,p}^2} = 2.716,$ which might make
sense in context. Computation in R:
sqrt(qchisq(.975, 2))
[1] 2.716203

However, a more common use of subscript notation with $\chi^2$
is that the probability in the subscript is cut from the lower tail of the distribution (a 'percentage point'). Then the quantity would be $0.225.$
sqrt(qchisq(.025, 2))
[1] 0.2250236

Note: The author quotes several well-known statisticians as being opposed
to the removal of outliers, unless traced to a specific mistake. Then
seems to ignore this advice with various suggestions for detecting and
removing inconvenient outliers from multivariate data. 
