A regression problem for continuous time series

N. P. Rasulov   ; A. S. Holevo

Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 4, pp. 762-771

Résumé

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 $|\lambda|^{2\alpha}$.