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Root-n-Consistent Estimation in Partial Linear Models with Long-Memory Errors

Jan Beran and Sucharita Ghosh
Scandinavian Journal of Statistics
Vol. 25, No. 2 (Jun., 1998), pp. 345-357
Stable URL: http://www.jstor.org/stable/4616506
Page Count: 13
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Root-n-Consistent Estimation in Partial Linear Models with Long-Memory Errors
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Abstract

We consider estimation of β in the semiparametric regression model $y(i)=x^{\text{T}}(i)\beta +f(i/n)+c(i)$ where x(i) = g(i/n) + e(i), f and g are unknown smooth functions and the processes ε(i) and e(i) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a √n-consistent estimator of β. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and √n-consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method.

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