Estimation of the Gauss-Markov process from observation of its sign

David Slepian

Stochastic Processes and their Applications, 1983, vol. 14, issue 3, 249-265

Abstract: Let X(t) be the ergodic Gauss-Markov process with mean zero and covariance function e-[tau]. Let D(t) be +1, 0 or -1 according as X(t) is positive, zero or negative. We determine the non-linear estimator of X(t1) based solely on D(t), -T [less-than-or-equals, slant] t [less-than-or-equals, slant] 0, that has minimal mean-squared error [var epsilon]2(t1, T). We present formulae for [var epsilon]2(t1, T) and compare it numerically for a range of values of t1 and T with the best linear estimator of X(t1) based on the same data.

Keywords: Optimal; estimation; stochastic; inference; optimal; prediction; Gauss--Markov; process (search for similar items in EconPapers)
Date: 1983
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