Many applications in statistics, economics, and physics require sampling from high-dimensional categorical distributions with local dependence structures. Examples include finite memory language models, Ising and Potts systems in statistical physics and protein folding, etc. In modern machine learning, discrete diffusi...
The estimation of sums of functions of observable and unobservable variables is a long-standing problem in statistics, with applications in many domains. We consider this problem in Poisson mixture models, where empirical Bayes provides a natural framework but nonparametric theory remains limited. We develop a nonparam...
Rates of convergence in normal approximation are fundamental to probability and statistics. The theory has evolved from normalized sums to Studentized statistics, smooth functions of sample means, and $U$-statistics, and more generally to symmetric statistics. A central question throughout this development has been to...
We prove two deterministic results for families of distances arising in the study of canonical processes. The first derives an admissible partition scheme from a growth condition. The second gives a representation in terms of parameterized separation trees and compares it with the corresponding majorizing-measure quant...
We study statistical inference for least squares estimators (LSEs) in additive monotone models under a general fixed lattice design. We establish joint limiting distributions for the LSEs and show that the estimators of different additive components are asymptotically independent. The form of the limiting distribution...
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