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Root-n-consistent Estimation in Partial Linear Models with Long-memory Errors
Authors:Jan Beran  & Sucharita Ghosh
Institution:University of Konstanz,;WSL, Switzerland
Abstract:We consider estimation of β in the semiparametric regression model y ( i ) - x T( i )β + f ( i / n ) + ε( 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
Keywords:long memory  long-range dependence  partial linear model  semiparametric estimation  semiparametric regression
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