## The Annals of Statistics

### A Sieve Estimator for the Mean of a Gaussian Process

Jay H. Beder

#### Abstract

A new sieve estimator for the mean function $m(t)$ of a general Gaussian process of known covariance is presented. The estimator $\hat{m}(t)$ is given explicitly from the data and has a simple distribution. It is shown that $\hat{m}(t)$ is asymptotically unbiased and consistent (weakly and in mean square) at each $t$, and that $\hat{m}$ is strongly consistent for $m$ in an appropriate norm. No assumptions are made about the "time" parameter or the covariance.

#### Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 59-78.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350253

Digital Object Identifier
doi:10.1214/aos/1176350253

Mathematical Reviews number (MathSciNet)
MR885724

Zentralblatt MATH identifier
0619.62078

JSTOR