Checking validity of monotone domain mean estimators

TL;DR

This paper introduces a diagnostic tool called CICs to assess the validity of monotonicity assumptions in domain mean estimators, improving estimation accuracy when assumptions hold and avoiding bias when they do not.

Contribution

The paper develops the Cone Information Criterion for Survey Data (CICs), a new method to test and decide on the appropriateness of monotonicity constraints in domain mean estimation.

Findings

CICs provides a consistent test for monotonicity departures.

The method improves estimation efficiency when constraints are valid.

It helps avoid bias by detecting incorrect shape assumptions.

Abstract

Estimates of population characteristics such as domain means are often expected to follow monotonicity assumptions. Recently, a method to adaptively pool neighboring domains was proposed, which ensures that the resulting domain mean estimates follow monotone constraints. The method leads to asymptotically valid estimation and inference, and can lead to substantial improvements in efficiency, in comparison with unconstrained domain estimators. However, assuming incorrect shape constraints could lead to biased estimators. Here, we develop the Cone Information Criterion for Survey Data (CICs) as a diagnostic method to measure monotonicity departures on population domain means. We show that the criterion leads to a consistent methodology that makes an asymptotically correct decision choosing between unconstrained and constrained domain mean estimators.