  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.
