A regression problem for continuous time series
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 4, pp. 762-771
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A model of observation
$$
\xi(t)=mt^{\nu}+\Delta(t),\qquad t\in[0,T],
$$
is considered, where $\nu$ is a non-negative integer, $\Delta(t)$ is a stationary process with zero mean
and with the spectral density of the form
$$
f(\lambda)=|\lambda|^{2\alpha}g(\lambda),\qquad \alpha>-1/2,\qquad g(0)>0.
$$
An asymptotically efficient estimate for the parameter $m$ is constructed as the pseudobest estimate corresponding to the generalized spectral density $|\lambda|^{2\alpha}$.
@article{TVP_1978_23_4_a4,
author = {N. P. Rasulov and A. S. Holevo},
title = {A regression problem for continuous time series},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {762--771},
publisher = {mathdoc},
volume = {23},
number = {4},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_4_a4/}
}
N. P. Rasulov; A. S. Holevo. A regression problem for continuous time series. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 4, pp. 762-771. http://geodesic.mathdoc.fr/item/TVP_1978_23_4_a4/