Nonparametric Estimation in a Model with a Trend |
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Authors: | Shen Jia Huang Yun‐Min |
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Institution: | (1) Department of Statistics and OR, Fudan University, Shanghai, China;(2) Department of Mathematics, Fudan University, Shanghai, China |
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Abstract: | Let Yt be a stochastic process taking values in R and defined by the model Yt=azt+ (Xt)+ t where {zt} is a deterministic sequence, {Xt} is strictly stationary and strongly mixing, and { t} is i.i.d. We study asymptotic properties of nonparametric estimators of density and regression with rates of convergence, and their behavior on estimation when ( ) is polynomial. It is shown that the estimator of the coefficients of ( ) constructed from the nonparametric estimators of regression is consistent when the deterministic {zt} converges in Cesàro mean, and may be inconsistent when {zt} is periodic under some ordinary conditions. |
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Keywords: | Mathematics Subject Classifications (1991): 62G07 62G20 nonparametric estimators of density and regression nonstationarity strongly mixing inconsistency of estimators |
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