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Array Normal Model and Incomplete Array Variate Observations

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Applied Matrix and Tensor Variate Data Analysis

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Abstract

Missing data present an important challenge when dealing with high-dimensional data arranged in the form of an array. The main purpose of this article is to introduce methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data imputation, estimation of mean, and covariance parameters for multiway data. A review of array variate distributions is included. A multiway semi-parametric mixed-effects model that allows separation of multiway mean and covariance effects is also defined, and an efficient algorithm for estimation based on the spectral decompositions of the covariance parameters is recommended. We demonstrate our methods with simulations and real-life data involving the estimation of genotype and environment interaction effects on possibly correlated traits.

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Acknowledgments

This research was supported by the USDA-NIFA-AFRI Triticeae Coordinated Agricultural Project, award number 2011-68002-30029.

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Authors and Affiliations

  1. Department of Plant Breeding and Genetics, Cornell University, Ithaca, NY, USA

    Deniz Akdemir

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  1. Deniz Akdemir
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Correspondence to Deniz Akdemir .

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  1. Faculty of Design, Kyushu University, Fukuoka, Fukuoka, Japan

    Toshio Sakata

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Akdemir, D. (2016). Array Normal Model and Incomplete Array Variate Observations. In: Sakata, T. (eds) Applied Matrix and Tensor Variate Data Analysis. SpringerBriefs in Statistics(). Springer, Tokyo. https://doi.org/10.1007/978-4-431-55387-8_5

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