Density estimation for shift-invariant multidimensional distributions

Understand

We study density estimation for classes of shift-invariant distributions over $\mathbb{R}^d$.

• A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any direction.
• Shift-invariance relaxes smoothness assumptions commonly used in non-parametric density estimation to allow jump discontinuities.
• The different classes of distributions that we consider correspond to different rates of tail decay.