High dimensional semiparametric latent graphical model for mixed data

Jianqing Fan Han Liu Yang Ning Hui Zou

Statistics Theory and Methods mathscidoc:1912.43333

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79, (2), 405-421
We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main contributions: we propose a unified rankbased approach to estimate the correlation matrix of latent variables; we establish the concentration inequality of the proposed rankbased estimator. Consequently, our methods achieve the same rates of convergence for precision matrix estimation and graph recovery, as if the latent variables were observed. The methods proposed are numerically assessed through extensive simulation studies, and real
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@inproceedings{jianqinghigh,
  title={High dimensional semiparametric latent graphical model for mixed data},
  author={Jianqing Fan, Han Liu, Yang Ning, and Hui Zou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113751769994893},
  booktitle={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={79},
  number={2},
  pages={405-421},
}
Jianqing Fan, Han Liu, Yang Ning, and Hui Zou. High dimensional semiparametric latent graphical model for mixed data. Vol. 79. In Journal of the Royal Statistical Society: Series B (Statistical Methodology). pp.405-421. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113751769994893.
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