The Dantzig selector for a linear model of diffusion processes

Kou Fujimori ()
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Kou Fujimori: Waseda University

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 5, 475-498

Abstract: Abstract In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional and sparse settings. To estimate drift matrices, the Dantzig selector which was proposed by Candés and Tao in 2007 will be applied. We will prove two types of consistency of the Dantzig selector for the drift matrix; one is the consistency in the sense of $$l_q$$ l q norm for every $$q \in [1,\infty ]$$ q ∈ [ 1 , ∞ ] and another is the variable selection consistency. Moreover, we will construct an asymptotically normal estimator for the drift matrix by using the variable selection consistency of the Dantzig selector.

Keywords: Diffusion process; High-dimension; Sparse estimation; Variable selection; Dantzig selector; 62H12; 62F12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11203-018-9191-y

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