Strong approximations for empirical processes indexed by Lipschitz functions
由 Lipschitz 函数索引的经验过程强逼近
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on d-variate random vectors (d≥1). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by Rio (Probab. Theory Related Fields 98 (1994) 21–45), and if the function class is Lipschitzian, our result…