Title: The Dantzig selector for a linear model of diffusion processes,
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 $q \in [1,\infty]$ 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.