The Dantzig selector for a linear model of diffusion processes

2017/09/03 by Fujimori, Kou · 1 citation
#62H12 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1709.00710

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. Then, we will prove two types of consistency of the estimator of drift matrix; one is the consistency in the sense of l_q norm for every q ∈ [1,∞] and the other is the variable selection consistency. Moreover, we will construct an asymptotically normal estimator of the drift matrix by using the variable selection consistency of the Dantzig selector.

Cited by

• Sparse estimation for the drift of high-dimensional Ornstein--Uhlenbeck processes with i.i.d. paths

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