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第
36
卷
2
期
2013
年
3
月
安徽师范大学学报(自然科学版)
Journal of
Anh
ui
Nonnal University (Natural
Sc
ience)
Vo
1.
36
No.2
Mar.2013
Moment Consistency
of
Estimators
in
Heteroscedastic
Partially
Linear
Model Under
Martingale
Difference
Errors
LI Shuai, F
AN
Guo-liar
毯,
T ANG Shi-bing
(Sc
h
∞
1
of Mathematics & Physics,
Anh
ui
Polytechnic University, Wuhu 241000 , China)
Abstract:
This
paper studies
the
heteroscedastic partially linear regression model under martingale
difference errors. Based
on
the
nonparametric estimates,
we
derive
the
least-squares estimator and
weighted least-squares estimator
of
slope
parameter
,'
and
obtain their
moment
consistencies under some
mild conditions.
Finite
sample behavior
of
the
estimators is investigated via simulations
t
∞·
Key
WOI
由
martingale
difference; heteroscedastic partially linear regression model; moment
consistency; least-squares
estimator;
weighted least-squares estimator
Classification
No:0212.
7
Doc
ument
code:A
Paper
No:1001-2443(2013)02
一
0103
-07
Introduction
In
general, a partiaIly linear
or
semiparametric regression model can be
written
出
Yi = x
J3
+ g
(tJ
+
句
1
三三
i
::Ç
n
,
、、,
J
咽
'A
J'1
、
where
βis
an unknown
parameter
of interest,
(Xi'
tj)
are nonrandom design points, Yi
are
the
r
臼
ponse
variabl
白,
g ( • ) is an
unknown
function defined
on
the
closed interval
[0
,
1]
,
Ci
are random errors.
Model
(1) which was first introduced
by
Engle
et
aI. (1
986)
has been widely studied in
the
literature and
them
勾
ority
of
the
work
done so far assumed
that
the
errors
Ci
are
independent and identically distributed
(i.
i.
d.
),
see Speckman
(1
988)
and
the
monograph of Härdle
et
al.
(2000)
among others. However,
the
independence assumption for
the
errors
is
not
always appropriate in application.
When
the
errors are assumed to
be
negatively associated random variables,
the
investigation related
to
the
model
(1)
can be found in Liang
et
al.
(2006)
, Liang and
Fan
(2009)
and
Fan
et
al.
(200
1).
In
particular,
many
authors investigated
the
model (1)
when
the
errors is a sequence of martingale differences, see Li and Liu
(2007)
, Chen and Cui
(2008)
and Fan
and
Liang
(2010)
among others. Meanwhile, heteroscedasticity also has been applied
to
the
model (1) by many
researchers
, see Y ou
et
aI.
(2007)
and
Liang
and
Ji
昭
(2009)
among others.
To
the
best of
our
knowledge,
the
moment
consistency for
the
estimators
of
卢
and
g(
. ) in
the
heteroscedastic partialIy linear
r.
唔
ression
model
(1)
with
martingale difference errors have not been studied.
The
pu
叩
ose
of this paper is
to
derive
the
moment consistency for
the
estimators
of
卢
and
g (
.)
in
the
heteroscedastic partia
lI
y linear regression model
(1)
with
martingale difference errors. More precisely, we
consider
the
heteroscedastic partially linear regression model (1) under the
fo
Ilowing error settings:
Ci
=刃而
ez:=
啊,
(2)
where
f(
.)
is a continuous function defined on
[0
, 1 ]
are
fixed design points and j e;
,g;
I
is
a
s
吨
uence
of
martingale difference
with
Received
date:2012-05
一
28
FO
Wl
dation item: Supported
by
the National Natural
Sc
ience Foundation of China (71171003) , Provincial Natural
Sc
ience Research Project of
Anh
ui
Co
lleges (KJ2011A032) ,
A
址
mi
Polytechnic University Foundation for Recruiting Talent (2011
YQω04)
,
Anh
ui
Provincial Natural
Sc
ienice Foundation (1208085QA04) ,
Anh
ui
Nonnal University
postdoctoral
阳
sitions
funded.
Author'
s brief: Li Shuai
(I
987 -
),
male , bom
in
Weinan city,
Sh
缸1X
l
provmce, master.
引用格式:李帅,范国良,唐仕冰.鞍差误差下异方差部分线性回归模型估计的矩相合性[]].安徽师范大学:自然科学版,
20
日,
36(2):
103
一
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