Connecting modelbased and modelfree approaches to linear least squares regression
Abstract
In a regression setting with response vector $\mathbf{y} \in \mathbb{R}^n$ and given regressors $\mathbf{x}_1,\ldots,\mathbf{x}_p \in \mathbb{R}^n$, a typical question is to what extent $\mathbf{y}$ is related to these regressors, specifically, how well can $\mathbf{y}$ be approximated by a linear combination of them. Classical methods for this question are based on statistical models for the conditional distribution of $\mathbf{y}$, given the regressors $\mathbf{x}_j$. In the present paper it is shown that various pvalues resulting from this modelbased approach have also a purely dataanalytic, modelfree interpretation. This finding is derived in a rather general context. In addition, we introduce equivalence regions, a reinterpretation of confidence regions in the modelfree context.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 DOI:
 10.48550/arXiv.1807.09633
 arXiv:
 arXiv:1807.09633
 Bibcode:
 2018arXiv180709633D
 Keywords:

 Mathematics  Statistics Theory;
 62J05