# An analysis of the SPARSEVA estimate for the finite sample data case

## TL;DR

This paper develops a theoretical upper bound for the SPARSEVA estimation error in finite sample scenarios, applicable to strongly convex cost functions and decomposable regularizers, with numerical validation.

## Contribution

It introduces a general upper bound for SPARSEVA error applicable to broad conditions and demonstrates its application to sparse regression problems.

## Key findings

- The derived bound effectively estimates the SPARSEVA error.
- Numerical results confirm the bound's accuracy and usefulness.
- The approach extends SPARSEVA analysis to finite sample data cases.

## Abstract

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound for the traditional SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.