Confidence limits for the parameter $\lambda$ of a~complex stationary Gaussian Markovian process

M. Arató

Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 326-332

Résumé

Let $\zeta(t)=\xi(t)+t\eta(t)$ be complex process satisfying the stochastic differential equation (1.1) $$ d\zeta(t)=-\gamma\zeta(t)\,dt+d\chi(t), $$ where $y=\lambda-i\omega$, $\chi(t)=\varphi(t)+i\psi(t)$, $\varphi$ and $\psi$ are independent Wiener processes. We get the characteristic function (2.2) of the sufficient statistics $s_1^2$, $Ts_2^2$ of the unknown parameter $\varkappa=\lambda T$. The quantiles of the distribution function of the maximum likelihood estimator $\widehat\varkappa=\widehat\lambda T$ (see (2.1)) at the levels $p=0.999$; $0.99$; $0.975$; $0.95$; $0.90$; $0.10$; $0.05$; $0.025$; $0.01$; $0.001$ are tabulated. From here we can get the confidence limits for the parameter $\varkappa=\lambda T$ ($0.1\varkappa\le100$).