Goodness-of-fit test in a multivariate errors-in-variables model $AX=B$

TL;DR

This paper develops a goodness-of-fit test for a multivariate errors-in-variables model using total least squares, which is asymptotically chi-squared under the null hypothesis and analyzed for power under local alternatives.

Contribution

It introduces a new goodness-of-fit test for multivariate errors-in-variables models based on total least squares, with theoretical properties and power analysis.

Findings

Test is asymptotically chi-squared under null hypothesis

Power analysis under local alternatives provided

Method applicable to multivariable functional errors-in-variables models

Abstract

We consider a multivariable functional errors-in-variables model $AX\approx B$, where the data matrices $A$ and $B$ are observed with errors, and a matrix parameter $X$ is to be estimated. A goodness-of-fit test is constructed based on the total least squares estimator. The proposed test is asymptotically chi-squared under null hypothesis. The power of the test under local alternatives is discussed.