MAT 453 Lecture Notes - Lecture 1: Multivariate Statistics, Descriptive Statistics, Linear Combination
Document Summary
Yuezhe li, notebook for mat 456, multivariate statistics: why multivariate statistics, arrays, descriptive statistics. I data obeys normal distribution. (cid:80)n j=1(xji xi)(xjk xk) j=1(xji xi)2. Aug. 20 for continuous distribution, it is almost su cient & necessary condition r > 0 = positive correlation; r < 0 = negative correlation; Aug. 21 distance: for p (x1, x2), q(0, 0), euclidean distance: d(p, q) =(cid:112)x2 generally, for p (x1, x2, , xp), q(y1, y2, , yp), d(p, q) =(cid:112)(cid:80)p. 2 i=1(xi yi)2 statistical distance: de ne standard variances of each dimension as variables. 1 using two-dimensional plane as example: p (x1, x2), o(0, 0) x . 2 = x1 s11 x2 s22 (cid:113) x . 2 s22 then we have their statistical distance: d(o, p ) = All points are at a distance of c2 from origin: x2. 2: inner product: x = (x1, x2)t , y = (y1, y2)t , x t y = x1y1 + x2y2.
