Uniform Convergence Rate of
Estimators of Autocovariances in Partly Linear Regression Models
with Correlated Errors |
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Authors: | Jin-hong?You Email author" target="_blank">Gemai?ChenEmail author Min?Chen Xue-lei?Jiang |
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Institution: | (1) University of Regina, Regina, Saskatchewan, S4S 0A2, Canada;(2) University of Calgary, Calgary, Alberta, T2N 1N4, Canada;(3) Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China |
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Abstract: | Consider the partly linear regression model
, where y
i
’s are
responses,
are known and nonrandom design points,
is a compact
set in the real line
, β =
(β
1, ··· , β
p
)'
is an unknown parameter vector, g(·) is an unknown function and
{ε
i
} is a linear process,
i.e.,
, where
e
j
are i.i.d. random variables with zero
mean and variance
. Drawing upon B-spline estimation of g(·) and
least squares estimation of β, we construct estimators of the
autocovariances of {ε
i
}. The uniform
strong convergence rate of these estimators to their true values
is then established. These results not only are a compensation
for those of 23], but also have some application in modeling
error structure. When the errors {ε
i
} are
an ARMA process, our result can be used to develop a consistent
procedure for determining the order of the ARMA process and
identifying the non-zero coeffcients of the process. Moreover,
our result can be used to construct the asymptotically effcient
estimators for parameters in the ARMA error process.
Supported by the Knowledge Innovation Project of Chinese
Academy of Sciences (No. KZCX2-SW-118) and the National Natural
Science Foundation of China (No. 70221001). |
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Keywords: | Uniform strong convergence rate autocovariance and autocorrelation B-spline estimation correlated error partly linear regression model |
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