纵向数据下半参数回归模型的统计分析.pdf

J.Sys.Sci.&Math.Scis.
27(6)(2007,12),847–857

∗

£¢

(461000;100022)

¤¡

(100022)

Æ

Æ

Æ

MR(2000)62G05,62G20

1

Æ

yij=xijβ+g(tij)+eij,i=1,2,···,n,j=1,2,···,mi,(1.1)

p

∈×·
(xij,tij)RRβpg()[0,1]

···{···}
eijei=(ei1,ei2,,eimi),ei,i=1,2,,n

n

Σ

E(ei)=0,Var(ei)=i().N=mi.n

i=1

mi

β

g(·)M

[1–4].(xij,tij)

[5]

(xij,tij)xij

·
tijβg()

[6]

(xij,tij)

*(10571008),(0511013300)

(2007110033)

2005-09-02,2006-10-16.

84827

[7]

LiangZeger

[2,8]

(GEE)GEELinCarroll

Æ

GEE

(1.1);GEE

·

βg()β

·

g()

2

nmknmk
xij=xij−Wkl(tij)xkl,yij=yij−Wkl(tij)ykl,
k=1l=1k=1l=1

xi=(xi1,xi2,···,ximi),yi=(yi1,yi2,···,yimi),

xi=(xi1,xi2,···,ximi),yi=(yi1,yi2,···,yimi),

···
Wkl(t)=Wkl(t;t11,t12,,tnmn)

−

(1.1)yijxijβ=g(tij)+eij,

·

g()

nmk

gˇ(t)=Wkl(t)(ykl−xklβ).
k=1l=1

···

gˇ(ti)=gˇ(ti1),gˇ(ti2),,gˇ(timi),Vieiβ

n
−1
yi−xiβ−gˇ(ti)Viyi−xiβ−gˇ(ti)=min!.(2.1)

i=1

n
−1
xiVi(yi−xi