Optimal Berry-Esséen bound for maximum likelihood estimation of the drift parameter in α-Brownian bridge
Let T > 0 , α > 1 2 . In the present paper we consider the α -Brownian bridge defined as d X t = - α X t T - t d t + d W t , 0 ≤ t < T , where W is a standard Brownian motion. We investigate the optimal rate of convergence to normality of the maximum likelihood estimator (MLE) for the param...
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Published in | Journal of the Korean Statistical Society Vol. 50; no. 2; pp. 403 - 418 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Singapore
Springer Singapore
01.06.2021
|
Subjects | |
Online Access | Get full text |
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Summary: | Let
T
>
0
,
α
>
1
2
. In the present paper we consider the
α
-Brownian bridge defined as
d
X
t
=
-
α
X
t
T
-
t
d
t
+
d
W
t
,
0
≤
t
<
T
, where
W
is a standard Brownian motion. We investigate the optimal rate of convergence to normality of the maximum likelihood estimator (MLE) for the parameter
α
based on the continuous observation
{
X
s
,
0
≤
s
≤
t
}
as
t
↑
T
. We prove that an optimal rate of Kolmogorov distance for central limit theorem on the MLE is given by
1
|
log
(
T
-
t
)
|
, as
t
↑
T
. First we compute an upper bound and then find a lower bound with the same speed using Corollary 1 and Corollary 2 of Kim et al. (J Multivar Anal 155:284–304, 2017b) respectively. |
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ISSN: | 1226-3192 2005-2863 |
DOI: | 10.1007/s42952-020-00084-3 |