The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is unknown. Two tests based on post-change density estimation are developed for this problem, the window-limited non-parametric generalized likelihood ratio (NGLR) CuSum test and the non-parametric window-limited adaptive (NWLA) CuSum test. Both tests do not assume any knowledge of the post-change distribution, except that the post-change density satisfies certain smoothness conditions that allows for efficient non-parametric estimation. Also, they do not require any pre-collected post-change training samples. Under certain convergence conditions on the density estimator, it is shown that both tests are first-order asymptotically optimal, as the false alarm rate goes to zero. The analysis is validated through numerical results, where both tests are compared with baseline tests that have distributional knowledge.

翻译：考虑独立观测序列中的最快变化检测问题。假设变前分布已知，而变后分布未知。针对该问题，本文提出了两种基于变后密度估计的检测方法：窗口限制非参数广义似然比（NGLR）CuSum检验和非参数窗口限制自适应（NWLA）CuSum检验。两种检验均无需对变后分布有任何先验知识，仅需变后密度满足某些平滑条件以便进行高效的非参数估计。同时，它们也不需要预先收集变后的训练样本。在密度估计器满足特定收敛条件的前提下，研究表明当虚警率趋近于零时，这两种检验均具有一阶渐近最优性。通过数值结果验证了理论分析，并与具有分布先验知识的基准检验进行了对比。