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.
Publié le : 1987-03-14
Classification:
Consistency,
Gaussian dichotomy theorem,
maximum likelihood estimation,
reproducing kernel Hilbert space,
sieve,
62M09,
60G15,
60G30
@article{1176350253,
author = {Beder, Jay H.},
title = {A Sieve Estimator for the Mean of a Gaussian Process},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 59-78},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350253}
}
Beder, Jay H. A Sieve Estimator for the Mean of a Gaussian Process. Ann. Statist., Tome 15 (1987) no. 1, pp. 59-78. http://gdmltest.u-ga.fr/item/1176350253/