On the asymptotic normality for integrated square error of Wegman-Davies recursive density estimators
In this article, let { X n , n ≥ 1 } be a sequence of i.i.d. random variables with common probability density function f, and f ̂ n denotes a Wegman-Davies recursive density estimator f ̂ n ( x ) = 1 n h n 1 / 2 ∑ i = 1 n 1 h i 1 / 2 K ( x − X i h i ) , where K is a kernel function and { h i , i ≥ 1...
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| Published in | Communications in statistics. Theory and methods Vol. 54; no. 5; pp. 1328 - 1353 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
04.03.2025
Taylor & Francis Ltd |
| Subjects | |
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| Abstract | In this article, let
{
X
n
,
n
≥
1
}
be a sequence of i.i.d. random variables with common probability density function f, and
f
̂
n
denotes a Wegman-Davies recursive density estimator
f
̂
n
(
x
)
=
1
n
h
n
1
/
2
∑
i
=
1
n
1
h
i
1
/
2
K
(
x
−
X
i
h
i
)
,
where K is a kernel function and
{
h
i
,
i
≥
1
}
is a sequence of band-width parameters. The asymptotic normality for integrated square error of Wegman-Davies recursive density estimators are established by using martingale method. |
|---|---|
| AbstractList | In this article, let
{
X
n
,
n
≥
1
}
be a sequence of i.i.d. random variables with common probability density function f, and
f
̂
n
denotes a Wegman-Davies recursive density estimator
f
̂
n
(
x
)
=
1
n
h
n
1
/
2
∑
i
=
1
n
1
h
i
1
/
2
K
(
x
−
X
i
h
i
)
,
where K is a kernel function and
{
h
i
,
i
≥
1
}
is a sequence of band-width parameters. The asymptotic normality for integrated square error of Wegman-Davies recursive density estimators are established by using martingale method. In this article, let {Xn,n≥1} be a sequence of i.i.d. random variables with common probability density function f, and f̂n denotes a Wegman-Davies recursive density estimatorf̂n(x)=1nhn1/2∑i=1n1hi1/2K(x−Xihi),where K is a kernel function and {hi,i≥1} is a sequence of band-width parameters. The asymptotic normality for integrated square error of Wegman-Davies recursive density estimators are established by using martingale method. |
| Author | Ye, Jun Miao, Yu |
| Author_xml | – sequence: 1 givenname: Yu surname: Miao fullname: Miao, Yu organization: Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University – sequence: 2 givenname: Jun surname: Ye fullname: Ye, Jun organization: College of Mathematics and Information Science, Henan Normal University |
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| Cites_doi | 10.1214/aoms/1177728190 10.1016/0304-4149(82)90003-5 10.1214/aos/1176344616 10.2298/FIL2327391M 10.1016/B978-0-12-319350-6.50012-8 10.1214/aos/1176342996 10.1214/aoms/1177704472 10.1007/s001840300302 10.1007/s00184-007-0159-y 10.1016/0047-259X(84)90044-7 10.1109/TIT.1969.1054295 10.1016/0047-259X(87)90077-7 10.5109/13049 |
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| References | Miao Y. (e_1_3_3_9_1) 2020; 40 Csörgő M. (e_1_3_3_2_1) 1981 Takahata H. (e_1_3_3_15_1) 2004; 56 e_1_3_3_7_1 e_1_3_3_6_1 e_1_3_3_8_1 e_1_3_3_18_1 e_1_3_3_17_1 e_1_3_3_14_1 e_1_3_3_13_1 e_1_3_3_16_1 e_1_3_3_3_1 e_1_3_3_10_1 e_1_3_3_5_1 Mokkadem A. (e_1_3_3_11_1) 2006; 32 e_1_3_3_12_1 e_1_3_3_4_1 |
| References_xml | – volume: 56 start-page: 1 year: 2004 ident: e_1_3_3_15_1 article-title: Central limit theorem for integrated square error of recursive density estimators publication-title: Bulletin of Tokyo Gakugei University – volume: 32 start-page: 323 year: 2006 ident: e_1_3_3_11_1 article-title: Large and moderate deviations principles for recursive kernel estimator of a multivariate density and its partial derivatives publication-title: Serdica Mathematical Journal – ident: e_1_3_3_13_1 doi: 10.1214/aoms/1177728190 – ident: e_1_3_3_3_1 doi: 10.1016/0304-4149(82)90003-5 – ident: e_1_3_3_16_1 doi: 10.1214/aos/1176344616 – volume-title: Strong approximations in probability and statistics year: 1981 ident: e_1_3_3_2_1 – volume: 40 start-page: 83 year: 2020 ident: e_1_3_3_9_1 article-title: Moderate deviation and large deviation for Wegman-Davies recursive density estimators publication-title: Probability and Mathematical Statistics – ident: e_1_3_3_10_1 doi: 10.2298/FIL2327391M – ident: e_1_3_3_5_1 doi: 10.1016/B978-0-12-319350-6.50012-8 – ident: e_1_3_3_14_1 doi: 10.1214/aos/1176342996 – ident: e_1_3_3_12_1 doi: 10.1214/aoms/1177704472 – ident: e_1_3_3_6_1 doi: 10.1007/s001840300302 – ident: e_1_3_3_7_1 doi: 10.1007/s00184-007-0159-y – ident: e_1_3_3_4_1 doi: 10.1016/0047-259X(84)90044-7 – ident: e_1_3_3_17_1 doi: 10.1109/TIT.1969.1054295 – ident: e_1_3_3_8_1 doi: 10.1016/0047-259X(87)90077-7 – ident: e_1_3_3_18_1 doi: 10.5109/13049 |
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| Snippet | In this article, let
{
X
n
,
n
≥
1
}
be a sequence of i.i.d. random variables with common probability density function f, and
f
̂
n
denotes a Wegman-Davies... In this article, let {Xn,n≥1} be a sequence of i.i.d. random variables with common probability density function f, and f̂n denotes a Wegman-Davies recursive... |
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| StartPage | 1328 |
| SubjectTerms | Asymptotic methods Asymptotic normality Asymptotic properties Estimators integrated square error Kernel functions martingale Martingales Normality Probability density functions Random variables recursive density estimators Recursive functions |
| Title | On the asymptotic normality for integrated square error of Wegman-Davies recursive density estimators |
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