Consistent estimation of joint distributions for sufficiently mixing random fields
充分混合随机场联合分布的一致估计
The joint distribution of a d-dimensional random field restricted to a box of size k can be estimated by looking at a realization in a box of size $n \gg k$ and computing the empirical distribution. This is done by sliding a box of size k around in the box of size n and computing frequencies. We show that when $k = k(n)$ grows as a function of n, then the total variation distance between this empirical distribution and the true distribution goes to 0 a.s. as $n \to \infty$ pr…