Timeline for Distribution of an observation-level Mahalanobis distance
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| S Jan 27, 2013 at 9:51 | history | suggested | CommunityBot | CC BY-SA 3.0 |
The formula gives the distance squared rather than the distance, a distinction often omitted in literature that is confusing to people learning the topic.
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| Jan 27, 2013 at 3:11 | answer | added | Joe Sullivan | timeline score: 13 | |
| Jan 27, 2013 at 3:03 | review | Suggested edits | |||
| S Jan 27, 2013 at 9:51 | |||||
| May 15, 2012 at 18:45 | comment | added | shabbychef | Can this result be used to find outlier observations in a Hotelling analysis? By that I mean compute the beta CDF of the rescaled $d_i^2$, and look for values near 1. Could one characterize the rescaled $d_i^2$ as 'leverages' in some way? fascinating. | |
| Jan 4, 2012 at 16:19 | history | edited | user88 | CC BY-SA 3.0 |
edited title
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| Jan 4, 2012 at 14:17 | comment | added | user8331 | The distribution of $d_i^2(\bar X,S)$ is a beta, $n/(n-1)^2 d_i^2(\bar X,S) \sim B(p/2, (n-p-1)/2)$, but I'm still seeking for the distribution of $d^2_i(\mu, S)$. The distributions of the $d^2_i$'s are not independent. | |
| Jan 4, 2012 at 2:26 | history | tweeted | twitter.com/#!/StackStats/status/154388212079534081 | ||
| Jan 3, 2012 at 17:53 | vote | accept | StasK | ||
| Jan 3, 2012 at 17:48 | comment | added | StasK | @whuber, roughly along the lines of what jbowman said -- to indicate that this is an observation-level statistic (as opposed to a sample level statistic, like sample mean). | |
| Jan 3, 2012 at 17:35 | answer | added | vinux | timeline score: 23 | |
| Jan 3, 2012 at 16:57 | comment | added | jbowman | @whuber - perhaps to emphasize that it's calculated using an observation from the sample, not a new observation? | |
| Jan 3, 2012 at 16:48 | comment | added | whuber♦ | Yes, but what I find confusing is that all the $d_i^2$ must have the same distribution because of the iid assumption, so why maintain a separate subscript? | |
| Jan 3, 2012 at 16:33 | comment | added | StasK | @whuber, $d_i^2$ is a function of a random vector $X_i$, and hence is a random variable. Is that what you are asking? | |
| Jan 3, 2012 at 16:32 | comment | added | StasK | @cardinal, you are certainly right, I had a thought that it has to be bounded, but it slipped my mind when I was writing this up. A scaled multivariate beta? | |
| Jan 3, 2012 at 16:00 | comment | added | cardinal | Just a little off-the-cuff side note, but notice that $X_i - \bar{X}$ is ancillary with respect to $\mu$ and $\sum_i d_i^2(\bar{X},S)$ is equal to a fixed constant (should be $n-p$, or similar, I think) almost surely. | |
| Jan 3, 2012 at 15:35 | comment | added | whuber♦ | In the definition of $d_i^2$, do you still view $X_i$ as a random variable or are you now treating it as a fixed vector? Including the subscript suggests the latter, but that seems a little strange. | |
| Jan 3, 2012 at 15:33 | history | edited | whuber♦ | CC BY-SA 3.0 |
added 29 characters in body
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| Jan 3, 2012 at 15:13 | history | asked | StasK | CC BY-SA 3.0 |