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Abstract:
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The semiparametric Gaussian copula model has wide applications in econometrics, finance and statistics. Recently, many have considered applications of semiparametric Gaussian copula model in several high-dimensional learning problems. In this paper we propose a slightly modified normal score estimator and a new Winsorized estimator for estimating both nonparametric transformation functions and the correlation matrix of the semiparametric Gaussian copula model. Two new concentration inequalities are derived, based on which we show that the normal score estimator and the new Winsorized estimator are consistent when the dimension grows at an exponential rate of the sample size. The rank-based approach can consistently estimate the covariance or precision matrix and their functionals but not the transformation functions. As demonstration, we apply our theory to two high-dimensional learning problems: semiparametric Gaussian graphical model and semiparametric discriminant analysis.
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