Re: What's the Mahanalobis distance?

[dim.brumath]

It's a good definition for the MD, but for outliers identification MD is not
robust because of masking and swamping phenomena: outliers could have low MD
and high MD means not in each cases outliers. See eg Barnet V, Lewis T.
(1994). Outliers in statistical data. John Wiley and Sons, New-York.,
Rousseew PJ, Leroy AM. (1987). Robust regression and outlier detection. John
Wiley and Sons, New-York. or works about robust distances.

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Dr SAULEAU Erik-A.
DIM
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Lorenzo Camprini [EMAIL PROTECTED] a écrit dans le message :
[EMAIL PROTECTED]

 Teo ha scritto nel messaggio...

 Anyone knows in what consist the Mahanalobis distance??
 I have to measure the distance between two histograms...
 

 from the StatSoft website (Glossary):

 "Mahalanobis distance. One can think of the independent variables
 (in a regression equation) as defining a multidimensional space in which
 each observation can be plotted. Also, one can plot a point representing
 the means for all independent variables. This "mean point" in the
 multidimensional
 space is also called the centroid. The Mahalanobis distance is the
distance
 of a case from the centroid in the multidimensional space, defined by the
 correlated
 independent variables (if the independent variables are uncorrelated,
 it is the same as the simple Euclidean distance).
 Thus, this measure provides an indication of whether or not an observation
 is an outlier with respect to the independent variable values."

 Proper citation:
 StatSoft, Inc. (1999). Electronic Statistics Textbook. Tulsa, OK:
StatSoft.
 WEB: http://www.statsoft.com/textbook/stathome.html.

 Lorenzo Camprini
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 in a college-level school
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Re: What's the Mahanalobis distance?

[dim.brumath]

The Mahalanobis distance (MD) is distance between each observation and the
mean of the others.
For the obs. i MD(i)*MD(i)=(X(i)-mean(X))*inverse(S)*transpose(X(i)-mean(X))
where mean(X) is the mean of variables X, X(i) is values of variables X for
i, S is the variance-covariance matrix of X.
A relation with hat-matrix H is MD(i)*MD(i)=(n-1)*(h(ii)-1/n) where n is the
number of observations and h(ii) is the ii-th element of diag of the
hat-matrix H=X*inverse(transpose(X)*X)*transpose(X).

Hope this helps

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Dr SAULEAU Erik-A.
DIM
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E-Mail: [EMAIL PROTECTED]
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Teo [EMAIL PROTECTED] a écrit dans le message :
[EMAIL PROTECTED]
 Anyone knows in what consist the Mahanalobis distance??
 I have to measure the distance between two histograms...


 Thanks,

Teo.


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