# Goodness-of-fit testing the error distribution in multivariate indirect regression

## TL;DR

This paper introduces a goodness-of-fit test for the error distribution in multivariate indirect regression models, utilizing the Khmaladze transformation to achieve consistency and power against local alternatives.

## Contribution

It develops a novel test statistic based on the Khmaladze transformation for error distribution in multivariate indirect regression, with proven consistency and local power.

## Key findings

- Test statistic based on Khmaladze transformation effectively detects deviations.
- The test maintains power against local alternatives converging at the root-n rate.
- The method is theoretically validated for consistency and efficiency.

## Abstract

We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This goodness-of-fit test is consistent at the root-n rate of convergence, and the test can maintain power against local alternatives converging to the null at a root-n rate.