All Questions
Tagged with geometric-measure-theory probability-distributions
4 questions with no upvoted or accepted answers
3
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Second-Order Taylor Expansion of Wasserstein Metric and Related Metrics
Suppose that we have a parametric distribution $P_{\theta}$, which is indexed by the parameter $\theta \in \mathbb{R}^d$. Let $W\{\cdot,\cdot\}$ be the Wasserstein Metric between two distributions.
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Showing that $b$ is a inner point of $\mathcal{G}$ where $\mathcal{G}$ is a subset of $\mathbb{R}^{N+3}$ determined by $\mathcal{M}^{+}$
Let $(\Xi,\mathscr{E})$ be a measurable space, $(\mathbb{R_{+}},\mathfrak{B})$ other measurable space where $\mathfrak{B}$ a $\sigma$-algebra. We consider the measurable space $(\Xi\times\Xi\times\...
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Random projection increases the distance?
Consider two absolutely continuous random variables $X: \Omega \mapsto \mathbb{R}^d$ and $Y: \Omega \mapsto \mathbb{R}^d$ for probability spaces $(\Omega, \mathcal{F},p_X)$ and $(\Omega, \mathcal{F},...
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Absolute continuity of probability measures determined by dependence structure
We are on $\mathbb{R}^d$ with Borel $\sigma$-algebra. Let $\mu_1, ..., \mu_d$ be probability measures on $\mathbb{R}$ and $\Pi(\mu_1, \mu_2, ..., \mu_d)$ be the set of probability measures on $\mathbb{...