Premium
High dimensional semiparametric latent graphical model for mixed data
Author(s) -
Fan Jianqing,
Liu Han,
Ning Yang,
Zou Hui
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12168
Subject(s) - latent variable , latent class model , latent variable model , local independence , estimator , mathematics , probabilistic latent semantic analysis , copula (linguistics) , statistics , graphical model , gaussian , conditional independence , econometrics , computer science , artificial intelligence , physics , quantum mechanics
Summary 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 rank‐based approach to estimate the correlation matrix of latent variables; we establish the concentration inequality of the proposed rank‐based 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 data analysis.