DeepAI AI Chat
Log In Sign Up

Confidence set for group membership

by   Andreas Dzemski, et al.

This paper develops procedures for computing a confidence set for a latent group structure. We study panel data models with unobserved grouped heterogeneity where each unit's regression curve is determined by the unit's latent group membership. Our main contribution is a new joint confidence set for group membership. Each element of the joint confidence set is a vector of possible group assignments for all units. The vector of true group memberships is contained in the confidence set with a pre-specified probability. The confidence set inverts a test for group membership. This test exploits a characterization of the true group memberships by a system of moment inequalities. Our procedure solves a high-dimensional one-sided testing problem and tests group membership simultaneously for all units. We also propose a procedure for identifying units for which group membership is obviously determined. These units can be ignored when computing critical values. We justify the joint confidence set under N, T →∞ asymptotics where we allow T to be much smaller than N. Our arguments rely on the theory of self-normalized sums and high-dimensional central limit theorems. We contribute new theoretical results for testing problems with a large number of moment inequalities including an anti-concentration inequality for the quasi-likelihood ratio (QLR) statistic. Monte Carlo results indicate that our confidence set has adequate coverage and is informative. We illustrate the practical relevance of our confidence set in two applications.


Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for ε-Product Spaces

We prove hypercontractive inequalities on high dimensional expanders. As...

Subvector Inference in Partially Identified Models with Many Moment Inequalities

This paper considers inference for a function of a parameter vector in a...

A Note on High-Dimensional Confidence Regions

Recent advances in statistics introduced versions of the central limit t...

Joint Learning of Assignment and Representation for Biometric Group Membership

This paper proposes a framework for group membership protocols preventin...

High-dimensional statistical inferences with over-identification: confidence set estimation and specification test

Over-identification is a signature feature of the influential Generalize...

Moment Inequalities in the Context of Simulated and Predicted Variables

This paper explores the effects of simulated moments on the performance ...

Standardized Tests and Affirmative Action: The Role of Bias and Variance

The University of California recently suspended through 2024 the require...