Anytime variants of Dijkstra's and A* shortest path algorithms quickly produce a suboptimal solution and then improve it over time. For example, ARA* introduces a weighting value "epsilon" to rapidly find an initial suboptimal path and then reduces "epsilon" to improve path quality over time. In ARA*, "epsilon" is based on a linear trajectory with ad-hoc parameters chosen by each user. We propose a new Anytime A* algorithm, Anytime Nonparametric A* (ANA*), that does not require ad-hoc parameters, and adaptively reduces varepsilon to expand the most promising node per iteration, adapting the greediness of the search as path quality improves. We prove that each node expanded by ANA* provides an upper bound on the suboptimality of the current-best solution. We evaluate the performance of ANA* with experiments in the domains of robot motion planning, gridworld planning, and multiple sequence alignment. The results suggest that ANA* is as efficient as ARA* and in most cases: (1) ANA* finds an initial solution faster, (2) ANA* spends less time between solution improvements, (3) ANA* decreases the suboptimality bound of the current-best solution more gradually, and (4) ANA* finds the optimal solution faster. ANA* is freely available from Maxim Likhachev's Search-based Planning Library (SBPL).