By John Fox

ISBN-10: 0761922792

ISBN-13: 9780761922797

"This publication matches into a wanted area of interest: rigorous sufficient to provide complete rationalization of the ability of the S language, but available adequate to assign to social technological know-how graduate scholars with out worry of intimidation. it's a large stability of utilized statistical "firepower" and considerate rationalization. It meets all the vital mechanical wishes: each one instance is given intimately, code and information are freely on hand, and the nuances of types are given instead of simply the naked necessities. It additionally meets a few vital theoretical wishes: linear types, specific info research, an creation to using GLMs, a dialogue of version diagnostics, and valuable directions on writing custom-made features. "

-Jeff Gill, collage of Florida, Gainesville

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Extra info for An R and S-Plus Companion to Applied Regression

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II. f. 7), then its distribution is elliptically contoured. f. -~ _£ f(X) = 11:1 2 1<1>\ 2 h(tr«X - M)' 1:- l (X - M)<1>-l», 1 1 -2 -2 then we want to show that X - E p,n(M,1: ® <1>,'1'). Let Y = 1: (X - M)<1> . f. of Y is g(Y) = h(tr(Y'Y». Let y = vec(Y'). f. of y is gl(y) = h(y'y). The characteristic function of y is cI>y(t) = f exp(it'y) h(y'y)dy, lRpn CHAPTER 2 28 where t E ]Rpn. Next, we prove that if tl and t2 are vectors of dimension pn such that t~ tl = t~t2' then

Of Y is g(Y) = h(tr(Y'Y». Let y = vec(Y'). f. of y is gl(y) = h(y'y). The characteristic function of y is cI>y(t) = f exp(it'y) h(y'y)dy, lRpn CHAPTER 2 28 where t E ]Rpn. Next, we prove that if tl and t2 are vectors of dimension pn such that t~ tl = t~t2' then

Let X - Ep,n(O,Ip @ In,'l') with stochastic representation X '" rU. 6. 45 BASIC PROPERTIES X= Xm where Xi is Pi x n matrix, i = 1,... ,m. 11) and vec(U~) is uniformly distributed on Spin, i = 1,2,... ,m. PROOF: Since X '" rU, we have -rU Xm where r and U are independent. Thus it suffices to prove that CHAPTER 2 46 u'" Note that U does not depend on 'l', so we can choose 'l'(z) = exp (- ~), which means X - Np,n(O,Ip @ In). It follows that Xi - Npi,n(O,Ipi @ In) and Xi'S are mutually independent, i = l,...

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An R and S-Plus Companion to Applied Regression by John Fox


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