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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 2, Pages 326–332
(Mi tvp849)
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This article is cited in 6 scientific papers (total in 6 papers)
Short Communications
Confidence limits for the parameter $\lambda$ of a complex stationary Gaussian Markovian process
M. Arató Budapest
Abstract:
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 $\varkappa=\lambda T$ ($0.1<\varkappa\le100$).
Received: 02.09.1966
Citation:
M. Arató, “Confidence limits for the parameter $\lambda$ of a complex stationary Gaussian Markovian process”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 326–332; Theory Probab. Appl., 13:2 (1968), 314–320
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