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arXiv · 1306.6222

Ultimate efficiency of designs for processes of Ornstein-Uhlenbeck type

V. Lacko
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Abstract

For a process governed by a linear Ito stochastic differential equation of the form dX(t)=[a(t)+b(t)X(t)]dt + \sigma(t)dW(t) we prove an existence of optimal sampling designs with strictly increasing sampling times. We derive an asymptotic Fisher information matrix, which we take as a reference in assessing a quality of finite-point sampling designs. The results are extended to a broader class of Ito stochastic differential equations satisfying a certain condition. We give an example based on the Gompertz growth law refuting a generally accepted opinion that small-sample designs lead to a very high level of efficiency.

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V. Lacko. 2013-06-26. Ultimate efficiency of designs for processes of Ornstein-Uhlenbeck type. https://arxiv.org/abs/1306.6222

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