## The Annals of Statistics

- Ann. Statist.
- Volume 2, Number 6 (1974), 1095-1107.

### On Large-Sample Estimation for the Mean of a Stationary Random Sequence

#### Abstract

For a wide class of stationary random sequences possessing a spectral density function, the variance of the best linear unbiased estimator for the mean is seen to depend asymptotically only on the behavior of the spectral density near the origin. Asymptotically efficient estimators based only on this behavior may be chosen. For spectral densities behaving like $\lambda^\nu$ at the origin, $\nu > -1$ a constant, the minimum variance decreases like $n^{-\nu-1}$, where $n$ is the sample size. Asymptotically efficient estimators depending on $\nu$ are given. Finally, the consequences of over- or under-estimating the value of $\nu$ in choosing an estimator are considered.

#### Article information

**Source**

Ann. Statist., Volume 2, Number 6 (1974), 1095-1107.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342867

**Digital Object Identifier**

doi:10.1214/aos/1176342867

**Mathematical Reviews number (MathSciNet)**

MR368354

**Zentralblatt MATH identifier**

0296.62081

**JSTOR**

links.jstor.org

**Keywords**

62 55 Linear estimation stationary time series mean spectral density efficiency

#### Citation

Adenstedt, Rolf K. On Large-Sample Estimation for the Mean of a Stationary Random Sequence. Ann. Statist. 2 (1974), no. 6, 1095--1107. doi:10.1214/aos/1176342867. https://projecteuclid.org/euclid.aos/1176342867