The Dantzig selector for diffusion processes with covariates

TL;DR

This paper adapts the Dantzig selector for estimating parameters in a diffusion process model where the diffusion coefficient depends on covariates, demonstrating its consistency across various norms.

Contribution

It introduces a novel application of the Dantzig selector to diffusion processes with covariates and proves its $l_q$ consistency.

Findings

The estimator is consistent in $l_q$ norm for all $q \, \in \, [1, \infty]$.

The proposed method effectively estimates diffusion process parameters with covariates.

The approach extends the applicability of the Dantzig selector to stochastic differential equations.

Abstract

The Dantzig selector for a special parametric model of diffusion processes is studied in this paper. In our model, the diffusion coefficient is given as the exponential of the linear combination of other processes which are regarded as covariates. We propose an estimation procedure which is an adaptation of the Dantzig selector for linear regression models and prove the $l_q$ consistency of the estimator for all $q \in [1,\infty]$.