Tailored inference for finite populations: conditional validity and transfer across distributions

TL;DR

This paper develops a statistical inference framework for finite populations with known attributes, providing conditionally valid confidence intervals that are tailored to specific populations and transferable across different distributions.

Contribution

It introduces methods for finite population inference that achieve conditional validity and shorter intervals by leveraging attribute information, extending to partial data and new populations.

Findings

Confidence intervals are conditionally valid for the realized population.

Intervals are shorter than traditional super-population methods.

Methods are validated with simulated and real-world data.

Abstract

Parameters of sub-populations can be more relevant than super-population ones. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned with the impact of a policy in a particular state within a given population. In these cases, the focus is on a specific finite population, as opposed to an infinite super-population. Such a population can be characterized by fixing some attributes that are intrinsic to them, leaving unexplained variations like measurement error as random. Inference for a population with fixed attributes can then be modeled as inferring parameters of a conditional distribution. Accordingly, it is desirable that confidence intervals are conditionally valid for the realized population, instead of marginalizing over many possible draws of populations. We provide a statistical inference framework for parameters of finite populations with known attributes. Leveraging the attribute information, our estimators and confidence intervals closely target a specific finite population. When the data is from the population of interest, our confidence intervals attain asymptotic conditional validity given the attributes, and are shorter than those for super-population inference. In addition, we develop procedures to infer parameters of new populations with differing covariate distributions; the confidence intervals are also conditionally valid for the new populations under mild conditions. Our methods extend to situations where the fixed information has a weaker structure or is only partially observed. We demonstrate the validity and applicability of our methods using simulated and real-world data.