Efficient robust estimation for single-index mixed effects models with missing observations

Liugen Xue () and Junshan Xie ()
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Liugen Xue: Henan University
Junshan Xie: Henan University

Statistical Papers, 2024, vol. 65, issue 2, No 12, 827-864

Abstract: Abstract In this paper, we study the efficient robust estimation and empirical likelihood for a single-index mixed effects model with a subset of covariates and response missing at random. Three efficient robust estimators and empirical likelihood ratios for index coefficients are constructed using weighted, imputed and weighted-imputed method, their asymptotic properties are proved. Our results show that the three estimators are asymptotically equivalent, and a weighted-imputed empirical log-likelihood ratio is asymptotically chi-squared. An important feature of our methods is their ability to handle missing response and/or partially missing covariates. Some simulation studies and a real data example indicate that our methods have fine performance in finite sample, and are available in practice.

Keywords: Single-index mixed effects model; Missing observation; Weighted-imputed method; Bias-correction technique; Efficient robust estimator; Primary 62J05; secondary 62G15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01407-2

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