Shilo, L. V. Asymptotic properties of the arithmetic-mean estimator of a stationary random sequence. (English. Russian original) Zbl 0699.62030 Theory Probab. Math. Stat. 40, 151-157 (1990); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 126-132 (1989). Summary: The asymptotic properties of the arithmetic-mean estimator for the unknown mean of a stationary stochastic sequence are studied. Special attention is given to the way in which the existence of zeros of the spectral density influences the asymptotic behavior of the variance of the arithmetic-mean estimator as the number of observations increases. MSC: 62F12 Asymptotic properties of parametric estimators 62M09 Non-Markovian processes: estimation Keywords:increasing number of observations; discrete parameter; arithmetic-mean estimator; stationary stochastic sequence; existence of zeros of the spectral density; variance PDFBibTeX XMLCite \textit{L. V. Shilo}, Theory Probab. Math. Stat. 40, 151--157 (1989; Zbl 0699.62030); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 126--132 (1989)