2013/06/26 by Vladimı́r Lacko, Lacko, V.
Decision Sciences · Mathematics · #60H10 #62B15 #62K05 #FOS: Mathematics #Optimal Experimental Design Methods #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1306.6222
openalex publication_date 2013/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a process governed by a linear Ito stochastic differential equation of the form dX(t)=[a(t)+b(t)X(t)]dt + σ(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.