Nonparametric Pattern-Mixture Models for Inference with Missing Data

2019/04/24 by Yen‐Chi Chen, Chen, Yen-Chi, Mauricio Sadinle +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1904.11085

openalex publication_date 2019/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that require identifying restrictions. We introduce a nonparametric estimator of the full-data distribution based on the pattern-mixture model factorization. Our approach uses the empirical observed-data distribution and augments it with a nonparametric estimator of the missing-data distributions under a given identifying restriction. Our results apply to a large class of donor-based identifying restrictions that encompasses commonly used ones and can handle both monotone and nonmonotone missingness. We propose a Monte Carlo procedure to derive point estimates of functionals of interest, and the bootstrap to construct confidence intervals.

Citations

• Remarks on Some Nonparametric Estimates of a Density Function
• Nonparametric estimation of distributions with categorical and continuous data
• Inference and missing data
• Bootstrap Methods: Another Look at the Jackknife
• On Estimation of a Probability Density Function and Mode
• Sequentially additive nonignorable missing data modeling using auxiliary marginal information

Cited by

• Markov Missing Graph: A Graphical Approach for Missing Data Imputation

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• Nonparametric Statistical Inference and Imputation for Incomplete Categorical Data