Robust Bounded Influence Tests for Independent Non-Homogeneous Observations

TL;DR

This paper introduces a new class of robust hypothesis tests for independent non-homogeneous data using density power divergence, improving robustness against outliers and model misspecification.

Contribution

It develops a general framework for robust tests in non-i.i.d. settings, with bounded influence functions and high power, applicable to regression models.

Findings

Tests are highly robust to data contamination.

Proposed tests outperform likelihood ratio tests under outliers.

Method is effective for simple and generalized linear regression models.

Abstract

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model misspecification. In this paper, we consider the set-up of non-identically but independently distributed observations and develop a general class of test statistics for testing parametric hypothesis based on the density power divergence. The proposed tests have bounded influence functions, are highly robust with respect to data contamination, have high power against contiguous alternatives, and are consistent at any fixed alternative. The methodology is illustrated by the simple and generalized linear regression models with fixed covariates.