zbMATH — the first resource for mathematics

Estimation of a centrality parameter and random sampling time schemes. II: Applications. (English) Zbl 0788.62080
Summary: An ARMA stationary process is sampled according to a renewal process. While estimating a centrality parameter and using the criterion as in part I, ibid., No. 1, 67-78 (1990; Zbl 0719.62097), we investigate the optimal sampling law’s support. We prove that in most of the situations this support is finite, and we give numerical results.
62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: Link EuDML
[1] G. E. P. Box, G. M. Jenkins: Time Series Analysis: Forecasting and Control. Holden-Day San Francisco 1976. · Zbl 0363.62069
[2] CI. Deniau G. Oppenheim, M. CI. Viano: Estimation of a centrality parameter and random sampling times schemes. Part I: Necessary condition of optimality. Kybernetika 26 (1990), 1, 67-78. · Zbl 0719.62097 · www.kybernetika.cz · eudml:27375
[3] G. Oppenheim: Echantillonnage aléatoire d’un processus ARMA. C R. Acad. Sci. Ser. I. Math. 295 (1982), 403-406. · Zbl 0514.60044
[4] G. Oppenheim: These d’Etat. Université Paris V, 1983.
[5] M. B. Priestley: Spectral Analysis of Time Series. Academic Press, New York 1981. · Zbl 0537.62075
[6] P. M. Robinson: Continuous models fitting from discrete data. Direction in Time Series (Brillinger, 1978, pp. 263-278.
[7] W. Rudin: Analyse reelle et complexe. Masson, Paris 1975. · Zbl 0333.28001
[8] Y. Taga: The optimal sampling procedure for estimating the mean of stationary Markov processes. Ann. Inst. Statist. Math. (1965), 105-112. · Zbl 0161.15802 · doi:10.1007/BF02868160
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.