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Unformatted text preview: tiating with respect to diagonal matrix, is introduced: we obtain: wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 24/74 10/09/2013 Stat841  Wiki Cour se Notes Note that the and are both symmetric matrices, thus set the first derivative to zero, we obtain: Thus, where and . As a matter of fact, must have nonzero eigenvalues, because . Therefore, the solution for this question is as same as the previous case. The columns of the transformation matrix
k − 1 eigenvalues with respect to are exactly the eigenvectors that correspond to largest Generalization of Fis her's Linear Dis criminant
Fisher's linear discriminant (Fisher, 1936) is very popular among users of discriminant analysis.Some of the reasons for this are its simplicity and unnecessity of strict
assumptions. However it has optimality properties only if the underlying distributions of the groups are multivariate normal. It is also easy to verify that the discriminant rule
obtained can be very harmed by only a small number of outlying observations. Outliers are very hard to detect in multivariate data sets and even when they are detected
simply discarding them is not the most effcient way of handling the situation. Therefore the need for robust procedures that can accommodate the outliers and are not
strongly affected by them. Then, a generalization of Fisher's linear discriminant algorithm [[12] (http://www.math.ist.utl.pt/~apires/PDFs/APJB_RP96.pdf) ]is developed to
lead easily to a very robust procedure. Linear Regression Models  October 14, 2009
Regression analysis (http://en.wikipedia.org/wiki/Regression_analysis) is a general statistical technique for modelling and analyzing how a dependent variable changes
according to changes in independent variables. In classification, we are interested in how a label, , changes according to changes in .
We will start by considering a very simple regression model, the linear regression model.
General information on linear regression (http://en.wikipedia.org/wiki/Linear_regression)...
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