This article is cited in 7 papers

Short Communications

On the Estimation of the Mean in Stationary Processes

S. Ya. Vilenkin


Abstract: The variance of the estimate
$$m_{N+1}=\frac1{N+1}\sum_{i=0}^N\xi\left(\frac{i}{N}\cdot T\right)$$
of a mean of a stationary process $\xi(t)$ is shown to attain its minimum value for some finite $N$.

Received: 07.05.1959

 English version: Theory of Probability and its Applications, 1959, 4:4, 415–416