Precise asymptotics of error variance estimator in partially linear models |
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Authors: | Shao-jun Guo Min Chen Feng Liu |
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Institution: | (1) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China;(2) Department of Statistics, Chongqing Institute of Technology, Chongqing, 630000, China |
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Abstract: | In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression
models, y
i
= x
i
τ
β + g(t
i
) + ε
i
, 1 ≤ i ≤ n, {ε
i
, i = 1, ⋯ n} are i.i.d random errors with mean 0 and positive finite variance σ
2. Following the ideas of Allan Gut and Aurel Spătaru7,8] and Zhang21], on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm,
respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
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Keywords: | Precise asymptotics partially linear models error variance estimator |
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