# Asymptotics of an empirical bridge of regression on induced order statistics

## TL;DR

This paper introduces a new statistical test for linear regression models based on empirical bridges derived from induced order statistics, with proven convergence properties and chi-square type tests.

## Contribution

It presents a novel class of tests using empirical bridges for regression on concomitants, with theoretical proof of weak convergence to Gaussian processes.

## Key findings

- Empirical bridges converge weakly to Gaussian processes.
- Tests are of chi-square type and based on residual sums.
- Method provides a new approach for regression analysis on induced order statistics.

## Abstract

We propose a class of tests for linear regression on concomitants (induced order statistics). These tests are based on sequential sums of regression residuals. We self-center and self-normalize these sums. The resulting process is called an empirical bridge. We prove weak convergence of the empirical bridge in uniform metrics to a centered Gaussian process. The proposed tests are of chi-square type.