Goodness-of-Fit Tests for Censored and Truncated Data: Maximum Mean Discrepancy Over Regular Functionals

2026-02-08

AI Summary

This study addresses the challenges posed by truncated or censored data, where conventional nonparametric maximum likelihood–based goodness-of-fit tests often suffer from infeasibility, instability, or slow convergence. The authors propose the first omnibus test for composite hypotheses under random double truncation. Their approach leverages a pathwise differentiable Neyman orthogonal score process and constructs a maximum mean discrepancy–type statistic within a reproducing kernel Hilbert space. Critical values are calibrated via a multiplier bootstrap procedure. Theoretical analysis establishes the test’s asymptotic validity under both the null hypothesis and local alternatives. Extensive simulations and empirical analyses demonstrate that the method achieves accurate size control and high power across a variety of incomplete data settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the nonparametric maximum likelihood estimator are hindered by nonexistence, computational instability, or convergence rates too slow to support reliable calibration under composite nulls. We avoid these difficulties by constructing a regular (pathwise differentiable) Neyman-orthogonal score process indexed by test functions, and aggregating it over a reproducing kernel Hilbert space ball. This yields a maximum-mean-discrepancy-type supremum statistic with a convenient quadratic-form representation. Critical values are obtained via a multiplier bootstrap that keeps nuisance estimates fixed. We establish asymptotic validity under the null and local alternatives and provide concrete constructions for left-truncated right-censored data, current status data, and random double truncation; in particular, to the best of our knowledge, we give the first omnibus goodness-of-fit test for a parametric family under random double truncation in the composite-hypothesis case. Simulations and an empirical illustration demonstrate size control and power in practically relevant incomplete-data designs.

Problem

• goodness-of-fit
• censored data
• truncated data
• composite hypothesis
• parametric models

Innovation

• maximum mean discrepancy
• Neyman-orthogonal score
• censored and truncated data
• reproducing kernel Hilbert space
• multiplier bootstrap