A structural model on a hypercube represented by optimal transport

Tomonari Sei

研究成果: Article査読

抄録

We propose a flexible statistical model for high-dimensional quantitative data on a hypercube. Our model, the structural gradient model (SGM), is based on a one-to-one map on the hypercube that is a solution to an optimal transport problem. As we show with many examples, SGM can describe various dependence structures including correlation and heteroscedasticity. The likelihood function is explicitly expressed without any normalizing constant. Simulation of SGM is achieved through a direct extension of the inverse function method. The maximum likelihood estimation of SGM is reduced to the determinant-maximization known as a convex optimization problem. In particular, a lasso-type estimation is available by adding constraints. SGM is compared with graphical Gaussian models and mixture models.

本文言語English
ページ(範囲)1291-1314
ページ数24
ジャーナルStatistica Sinica
21
3
DOI
出版ステータスPublished - 2011 7月

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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