Abstract
This article discusses the extension to general compact Abelian groups of some results previously established by R. Roy for the case of the circle and the sphere. Estimators of the covariance function and spectral parameters for a homogeneous stochastic process defined on a compact Abelian group are considered and their properties are derived.
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References
Brillinger, D. R. (1975).Time Series—Data Analysis and Theory, Holt, Rinehart and Winston, N.Y.
Goodman, N. R. (1963). Statistical analysis based on a certain multivariate complex Gaussian distribution (An introduction),Ann. Math. Statist.,34, 152–177.
Hannan, E. J. (1971).Multiple Time Series, John Wiley and Sons, N.Y.
Jones, R. H. (1963). Stochastic processes on a sphere,Ann. Math. Statist.,34, 213–215.
Morettin, P. A. (1979). Homogeneous random processes on locally compact Abelian groups, to appear Annals of Braz. Academy of Sciences.
Pontryagin, L. S. (1966).Topological Groups, 2nd edition, Gordon and Breach, N.Y.
Roy, R. (1972). Spectral analysis for a random process on the circle,J. Appl. Prob.,9, 745–757.
Roy, R. (1973). Estimation of the covariance function of a homogeneous processes on the sphere,Ann. Statist.,1, 780–785.
Roy, R. (1976a). Spectral analysis for a random process on the sphere,Ann. Inst. Statist. Math.,28, 91–97.
Roy, R. and Dufour, J. M. (1976b). On spectral estimation for a homogeneous random process on the circle,Stoch. Processes Appl.,4, 107–120.
Yaglom, A. M. (1961). Second-order homogeneous random fields,Proc. Fourth Berkeley Symp., 593–622.
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Morettin, P.A. On homogeneous stochastic processes on compact Abelian groups. Ann Inst Stat Math 30, 465–472 (1978). https://doi.org/10.1007/BF02480236
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DOI: https://doi.org/10.1007/BF02480236