A non-asymptotic CLT is proved for projections of high-dimensional spin vectors satisfying Poincare inequality via martingale embedding, with 2-Wasserstein error bounds involving two- and three-point functions, and applications to Ising and SK models.
Stein couplings for normal approximation
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abstract
In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach, exchangeable pairs, size biasing and many other approaches. We prove several theorems with which normal approximation for the Wasserstein and Kolmogorov metrics becomes routine once a Stein coupling is found. To illustrate the versatility of our framework we give applications in Hoeffding's combinatorial central limit theorem, functionals in the classic occupancy scheme, neighbourhood statistics of point patterns with fixed number of points and functionals of the components of randomly chosen vertices of sub-critical Erdos-Renyi random graphs. In all these cases, we use new, non-standard couplings.
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Overlap-weighted ATE is bounded between ATT and ATC under monotonic PS-CATE relationship, with extensions to weighted LATE and other weights, recommending CP-plot of CATE vs PS.
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Central limit theorem for high temperature spin models via martingale embedding
A non-asymptotic CLT is proved for projections of high-dimensional spin vectors satisfying Poincare inequality via martingale embedding, with 2-Wasserstein error bounds involving two- and three-point functions, and applications to Ising and SK models.