Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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On the Optimal Adaptive Estimation in the Semiparametric Non-linear Autoregressive Time Series Model

  • So, Beong-Soo (Department of Statistics, Ewha Womens University, Seodaemun, Seoul 120-750)
  • Published : 1995.06.01
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Abstract

We consider the problem of optimal adaptive estiamtion of the euclidean parameter vector $\theta$ of the univariate non-linerar autogressive time series model ${X_t}$ which is defined by the following system of stochastic difference equations ; $X_t = \sum^p_{i=1} \theta_i \cdot T_i(X_{t-1})+e_t, t=1, \cdots, n$, where $\theta$ is the unknown parameter vector which descrives the deterministic dynamics of the stochastic process ${X_t}$ and ${e_t}$ is the sequence of white noises with unknown density $f(\cdot)$. Under some general growth conditions on $T_i(\cdot)$ which guarantee ergodicity of the process, we construct a sequence of adaptive estimatros which is locally asymptotic minimax (LAM) efficient and also attains the least possible covariance matrix among all regular estimators for arbitrary symmetric density.

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References

  1. The Annals of Statistics v.11 Information and asymptotic efficiency in parametric-nonparametric models Begun,J.M.;Hall,W.J.;Huang,W.M.;Wellner,J.A.
  2. The Annals of Institute of Statistical Mathematics v.28 Adaptive estimates for autoregressive processes Beran,R.
  3. Journal of Time Series Analysis v.7 no.3 On estimating thresholds in autoregressive models Chan,K.S.;Tong,H.
  4. The Annals of Statistics v.6 On conditional least squares estimation for stochastic processes Klimko,L.A.;Nelson,P.I.
  5. The Annals of Statistics v.15 On adaptive estimation in stationary ARMA-models Kreiss,J.P.
  6. Contiguity of Probability Measures:Some Applications in Statistics Roussas,G.
  7. Journal of Statistical Planning and Infeence v.16 A note on the construction of asymptotically linear estimators Schick,A.
  8. Lecture notes in Statistics. 21 Threshold Models in Non-linear Time Series Analysis Tong,H.
  9. Non-linear Time Series Tong,H.