About the Prohorov distance between the uniform distribution over the unit cube in \(R^ d\) and its empirical measure (Q1099480)
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scientific article; zbMATH DE number 4040938
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | About the Prohorov distance between the uniform distribution over the unit cube in \(R^ d\) and its empirical measure |
scientific article; zbMATH DE number 4040938 |
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About the Prohorov distance between the uniform distribution over the unit cube in \(R^ d\) and its empirical measure (English)
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1988
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We compute the almost sure order of convergence of the Prokhorov distance between the uniform distribution P over \([0,1]^ d\) and the empirical measure associated with n independent observations with (common) distribution P. We show that this order of convergence is \(n^{-1/d}\) up to a power of log(n). This result extends to the case where the observations are weakly dependent.
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order of convergence of the Prokhorov distance
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weakly dependent
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empirical measure
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