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Let $X_1, \cdots, X_n \sim \mathrm{Unif}[0,1]$ be $n$ random variables, each with marginal distribution being a standard uniform distribution. I want to characterize the set of covariance matrices (or correlation matrix if thisit is easier) that can be attained by these $n$ variables. Is there a simple characterization? I feel the set shouldmight be a polyhedron.

Let $X_1, \cdots, X_n \sim \mathrm{Unif}[0,1]$ be $n$ random variables, each with marginal distribution being a standard uniform distribution. I want to characterize the set of covariance matrices (or correlation matrix if this is easier) that can be attained by these $n$ variables. Is there a simple characterization? I feel the set should be a polyhedron.

Let $X_1, \cdots, X_n \sim \mathrm{Unif}[0,1]$ be $n$ random variables, each with marginal distribution being a standard uniform distribution. I want to characterize the set of covariance matrices (or correlation matrix if it is easier) that can be attained by these $n$ variables. Is there a simple characterization? I feel the set might be a polyhedron.

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zxzx179
zxzx179
  • 205
  • 1
  • 6

Covariance/Correlation matrix of $n$ random variables with uniform marginal distributions

Let $X_1, \cdots, X_n \sim \mathrm{Unif}[0,1]$ be $n$ random variables, each with marginal distribution being a standard uniform distribution. I want to characterize the set of covariance matrices (or correlation matrix if this is easier) that can be attained by these $n$ variables. Is there a simple characterization? I feel the set should be a polyhedron.