Abstract
The limiting distribution of the kernel error estimators in nonlinear autoregressive models is considered. It is shown that, at a fixed point, the distribution of the kernel error density estimator is normal without knowing the nonlinear autoregressive function.
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References
H.L. Koul, Weighted Empirical Processes in Dynamic Nonlinear Models. Lecture Notes in Statistics, vol. 166 (Springer, New York, 2002)
Koul, H.L.: A weak convergence result useful in robust autoregression. J. Stat. Plan. Inference 29, 291–308 (1991)
Koul, H.L., Osiander, M.: Weak convergence of randomly weighted residuals empiricals with application to autoregression. Ann. Stat. 22, 540–562 (1994)
Cheng, F.X.: Asymptotic distribution of error density estimators in first-order autoregressive models. Sankhyā. Indian J. Stat. 67(3), 553–567 (2005)
Brockwell, P.J., Davis, R.A.: Time Series: Thoery and Methods. Springer Series in Statistics. Springer-Verlag, New York (1991)
Klimko, L.A., Nelson, P.I.: On conditional least squares estimation for stochastic processes. Ann. Stat. 6, 629–642 (1978)
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Supported by the NNSF of China(10671176&10771192).
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Fu, K., Yang, X. Asymptotics of kernel error density estimators in nonlinear autoregressive models. J Math Chem 44, 831–838 (2008). https://doi.org/10.1007/s10910-008-9379-2
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DOI: https://doi.org/10.1007/s10910-008-9379-2