作者rpm (我永远的旭仔..)
站内Statistics
标题[问题] 2阶微分求极值的问题--有关regression
时间Mon Jun 5 12:20:20 2006
老师出了一题统计公课
因为实在远离数学太久了~~
可以请高手帮我解答或提示我那本参考书可以找到答案吗? 感激不尽 T T
题目是:
simple regression
sample:(x1,y1),(x2,y2),...(xn,yn)
Y=a+bx+ε
^ ^
E(Y)=a + b x
2
E~ N(0,σ )
n 2 n 2
L= Σ εi = Σ [yi-(a+b*xi)]
i=1 i=1
^ _ _ 2 _2
δL/δa=0 , δL/δb=0 证明:b =Σxiyi-nx y / Σxi - nx
^ _ ^ _
a = y- b * x
接下来还要证明下面四项,D式子我不太会微分 >"<
Let L be a function of two variables with continuous second-order partial
derivatives in some circle centered at a critical point(a,b)
2
and let D=Lxx(a,b)Lyy(a,b)-{Lxy(a,b)}
(I) if D > 0 , Lxx(a,b)>0 ,then L has a relative minimum at (a,b)
(II) if D > 0 , Lxx(a,b)<0 ,then L has a relative maximum at (a,b)
(III) if D < 0 , then L has a saddle point at (a,b)
(IV) if D = 0 , then no conclusion can be drown
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