Estimation of the covariance matrix with two-step monotone missing data

We suggest shrinkage based technique for estimating covariance matrix in the high-dimensional normal model with missing data. Our approach is based on the monotone missing scheme assumption, meaning that missing values patterns occur completely at random. Our asymptotic framework allows the dimensio...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 45; no. 7; pp. 1910 - 1922
Main Authors Hyodo, Masashi, Shutoh, Nobumichi, Seo, Takashi, Pavlenko, Tatjana
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.04.2016
Taylor & Francis Ltd
Subjects
62F12
62H12
Asymptotic properties
Covariance matrix
Dominance
Estimators
High-dimensional estimation
Infinity
Missing data
Monotone missing data
Simulation
Statistics
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Summary:We suggest shrinkage based technique for estimating covariance matrix in the high-dimensional normal model with missing data. Our approach is based on the monotone missing scheme assumption, meaning that missing values patterns occur completely at random. Our asymptotic framework allows the dimensionality p grow to infinity together with the sample size, N, and extends the methodology of Ledoit and Wolf (2004) to the case of two-step monotone missing data. Two new shrinkage-type estimators are derived and their dominance properties over the Ledoit and Wolf (2004) estimator are shown under the expected quadratic loss. We perform a simulation study and conclude that the proposed estimators are successful for a range of missing data scenarios.
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ISSN:0361-0926
1532-415X
1532-415X
DOI:10.1080/03610926.2013.868085