Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data

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• 作者：Ke-Hai Yuan ; Wai Chan ; Yubin Tian
• 关键词：Missing data ; Monte Carlo ; Robust means and dispersion matrix ; Sandwich ; type covariance matrix
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：68
• 期：2
• 页码：329-351
• 全文大小：581 KB
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• 作者单位：Ke-Hai Yuan (1)
  Wai Chan (2)
  Yubin Tian (3)
  
  1. Department of Psychology, University of Notre Dame, Notre Dame, IN, 46556, USA
  2. Department of Psychology, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
  3. School of Mathematics, Beijing Institute of Technology, Haidian District, Beijing, 100081, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Netherlands
• ISSN：1572-9052

文摘

Means and covariance/dispersion matrix are the building blocks for many statistical analyses. By naturally extending the score functions based on a multivariate \(t\)-distribution to estimating equations, this article defines a class of M-estimators of means and dispersion matrix for samples with missing data. An expectation-robust (ER) algorithm solving the estimating equations is obtained. The obtained relationship between the ER algorithm and the corresponding estimating equations allows us to obtain consistent standard errors when robust means and dispersion matrix are further analyzed. Estimating equations corresponding to existing ER algorithms for computing M- and S-estimators are also identified. Monte Carlo results show that robust methods outperform the normal-distribution-based maximum likelihood when the population distribution has heavy tails or when data are contaminated. Applications of the results to robust analysis of linear regression and growth curve models are discussed.