AI 中文总结
本文通过假设检验逆变换构造一致下置信界，结合均匀大数定律，证明了随设计点数量趋于无穷，该检验能以渐近概率1正确识别被低估的Lipschitz常数，完成了Lipschitz参数估计的收敛性证明。
AI 中文摘要
本文通过假设检验逆变换构造一致下置信界，给出了Lipschitz参数估计的证明。我们证明，当设计点数量趋于无穷时，该检验能以渐近概率1正确识别任何被低估的Lipschitz常数。收敛性证明依赖于均匀大数定律，并分析了有界与无界重复采样下的差异度量。
英文摘要
This document presents a proof of the estimation of a lipschitz parameter by constructing a consistent lower confidence bound through hypothesis test inversion. We prove that as the number of design points grows to infinity, the test correctly identifies any underestimated Lipschitz constant with asymptotic probability 1. The convergence proofs rely on a Uniform Law of Large Numbers and analyze discrepancy metrics under both bounded and unbounded replication sampling.
