Tuning Parameter-Free Nonparametric Density Estimation from Tabulated Summary Data

TL;DR

This paper introduces a tuning parameter-free nonparametric density estimator based on maximum entropy, designed for tabulated summary data, with proven consistency and practical application to income distribution estimation.

Contribution

It presents a novel, tuning-free density estimation method from summary data using maximum entropy, with theoretical guarantees and practical applicability.

Findings

Estimator is strongly uniformly consistent.

Provides a closed-form density for easy analysis.

Successfully applied to U.S. tax return data.

Abstract

Administrative data are often easier to access as tabulated summaries than in the original format due to confidentiality concerns. Motivated by this practical feature, we propose a novel nonparametric density estimation method from tabulated summary data based on maximum entropy and prove its strong uniform consistency. Unlike existing kernel-based estimators, our estimator is free from tuning parameters and admits a closed-form density that is convenient for post-estimation analysis. We apply the proposed method to the tabulated summary data of the U.S. tax returns to estimate the income distribution.