【摘 要】
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This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local H(o)lder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated;then we provide a linear wavelet es
【机 构】
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College of Mathematics,Faculty of Science,Beijing University of Technology,Beijing 100124,China
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This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local H(o)lder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated;then we provide a linear wavelet estimate to obtain the optimal convergence rate,which means that the convergence rate coincides with the lower bound.The non-linear wavelet estimator is introduced for adaptivity,although it is nearly-optimal.However,the non-linear wavelet one depends on an upper bound of the smoothness index of unknown functions,we finally discuss a data driven version without any assumptions on the estimated functions.
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