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Parameter estimation for finite-parameter stationary random fields

Published online by Cambridge University Press:  14 July 2016

M. Rosenblatt
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Abstract

The concept of strong mixing is used to obtain a generalization of results on the asymptotic distribution of finite-parameter estimates of linear processes and extend them for stationary sequences and random fields.

Keywords

STRONG MIXINGASYMPTOTIC DISTRIBUTIONSMOOTHED PERIODOGRAM
Type
Part 5—Random Fields and Point Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 311 - 318
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Donoho, D. (1981) On minimum entropy deconvolution. In Applied Time Series Analysis II , ed. Findley, D. F., Academic Press, New York, 565–608.Google Scholar
Hannan, E. J. and Heyde, C. C. (1972) On limit theorems for quadratic functions of discrete time series. Ann. Math. Statist. 43, 2058–2066.Google Scholar
Larimore, W. E. (1977) Statistical inference on stationary random fields. Proc. IEEE 65, 961–970.Google Scholar
Lu, K. S. and Rosenblatt, M. (1982) Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes. Ann. Statist. 10, 1195–1208.Google Scholar
Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. U.S.A. 42, 43–47.CrossRefGoogle Scholar
Rosenblatt, M. (1972) Central limit theorem for stationary processes. Proc. 6th Berkeley Symp. Math. Statist. Prob. 2, 551–561.Google Scholar
Rosenblatt, M. (1980) Linear processes and bispectra. J. Appl. Prob. 17, 265–270.CrossRefGoogle Scholar
Rosenblatt, M. (1985) Stationary Sequences and Random Fields. Birkhäuser-Verlag, Basel.Google Scholar
Walker, A. M. (1963) Asymptotic properties of least squares estimates of parameters of the spectrum of a stationary non-deterministic time-series. J. Austral. Math. Soc. 4, 363–384.Google Scholar
Whittle, P. (1954) A Study in the Analysis of Stationary Time Series. Almquist and Wiksell, Uppsala.Google Scholar
Wiggins, R. A. (1978) Minimum entropy deconvolution. Geoexploration 16, 21–35.Google Scholar