Koval’chuk, T. V. On convergence of the distributions of functionals of the correlogram of a homogeneous random field with unknown mean. (English. Russian original) Zbl 0634.62094 Theory Probab. Math. Stat. 35, 45-53 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 44-51 (1986). A theorem analogous to the invariance principle in the space of continuous functions is proved for an appropriately centralized and normalized estimator of the correlation function of homogeneous random fields with unknown expectation. Reviewer: M.Yadrenko MSC: 62M99 Inference from stochastic processes 62F12 Asymptotic properties of parametric estimators 60G60 Random fields 60F17 Functional limit theorems; invariance principles 62M09 Non-Markovian processes: estimation 62E20 Asymptotic distribution theory in statistics Keywords:observations on parallelepipeds; limit distribution; Gaussian measure; second- and fourth-order spectral densities; correlogram; strong mixing; invariance principle in the space of continuous functions; centralized and normalized estimator of the correlation function of homogeneous random fields with unknown expectation PDFBibTeX XMLCite \textit{T. V. Koval'chuk}, Theory Probab. Math. Stat. 35, 45--53 (1986; Zbl 0634.62094); translation from Teor. Veroyatn. Mat. Stat. 35, 44--51 (1986)