# Hypothesis testing in the presence of multiple samples under density ratio models

arXiv: https://arxiv.org/abs/1309.4740 · HTML: https://mlsanity.com/paper/1309.4740/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2013.

## Built on by (most cited first, 2 of 2)

- [A Semiparametric Approach to Causal Inference](https://mlsanity.com/paper/2411.00950/) (2024)
- [FedSPM: Routing-Enabled Federated Learning under Dual Heterogeneity via Semiparametric Mixture](https://mlsanity.com/paper/2607.04085/) (2026)

## Abstract (arXiv)

This paper presents a hypothesis testing method given independent samples from a number of connected populations. The method is motivated by a forestry project for monitoring change in the strength of lumber. Traditional practice has been built upon nonparametric methods which ignore the fact that these populations are connected. By pooling the information in multiple samples through a density ratio model, the proposed empirical likelihood method leads to a more efficient inference and therefore reduces the cost in applications. The new test has a classical chi-square null limiting distribution. Its power function is obtained under a class of local alternatives. The local power is found increased even when some underlying populations are unrelated to the hypothesis of interest. Simulation studies confirm that this test has better power properties than potential competitors, and is robust to model misspecification. An application example to lumber strength is included.