Convergence Properties of a Spectral Density Estimator

  • Gyeong Hye Shin (Lecturer, Department of mathematics, Yonsei University, Seoul, 120-749, Korea) ;
  • Hae Kyung Kim (Professor, Department of mathematics, Yonsei University, Seoul, 120-749, Korea)
  • Published : 1996.12.01


this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.



  1. Journal of Statistical Planning and Inference v.28 Nonparametric curve estimation with series errors Truong, Y. K.
  2. Annals of Statistics v.10 Optimal global rates of convergence for nonparametric regression Stone, C. J.
  3. Ph. D. Thesis, Yonsei Univ. Asymptotic convergence properties in spectral estimation Shin, G. H.
  4. Theory and Methods Brockwell, P. J.;Davis, R. A.
  5. Annals of Probability v.4 Asymptotic nomality, strong mixing and spectral density estimates Rosenblatt, M.