Parameter estimation of continuous-time stationary Gaussian processes with rational spectra (Q1099122)

The achievable accuracy in estimating the parameter vector Sc of the continuous-time spectral density from the sampled ARMA model is discussed. The sampling interval is T, and the sampled process has the parameter vector Sd of its discrete-time power spectral density. The lower bounds on the variance of the unbiased estimate of Sc and Sd are given by the Cramer-Rao bound, i.e., CRB(Sc) and CRB(Sd), and those two bounds satisfy the following relation \(CRB(Sc)=(\partial Sc/\partial Sd)(\partial Sc/\partial Sd)^ H\) where \((\cdot)^ H\) denotes a random specification of an agent's preference preordering. The set of random preference specifications which yield binary choice probabilities satisfying monotonic scalable choice (a restriction on choice probabilities commonly found in the spatial elections literature) is studied. We investigate whether imposing the restriction of monotonic scalable choice limits attention to random preference specifications which are knife-edge cases, so that an arbitrarily small perturbation in the agent's random preference specification causes the restriction to fail; or whether the restriction is robust to such perturbations. If the choice set is finite, the set of preference specifications satisfying monotonic scalable choice is closed, but has an interior of positive measure. Hence, the assumption need not be a knife-edge formulation. If the choice set is infinite, the set of preference specifications satisfying monotonic scalable choice has no interior points (and is closed), and thus is a knife-edge formulation.