The problem of estimating a piecewise monotone sequence of normal means is called the nearly isotonic regression. For this problem, an efficient algorithm has been devised by modifying the pool adjacent violators algorithm (PAVA). In this study, we extend nearly isotonic regression to general one-parameter exponential families such as binomial, Poisson and chi-square. We consider estimation of a piecewise monotone parameter sequence and develop an efficient algorithm based on the modified PAVA, which utilizes the duality between the natural and expectation parameters. We also provide a method for selecting the regularization parameter by using an information criterion. Simulation results demonstrate that the proposed method detects change-points in piecewise monotone parameter sequences in a data-driven manner. Applications to spectrum estimation, causal inference and discretization error quantification of ODE solvers are also presented.

翻译：估计普通手段的单质单质单质序列的问题被称为近等离子回归。 对于这个问题,通过修改池群相邻的违反者算法(PAVA)设计了一个高效的算法。 在这项研究中,我们将近乎等离子回归法扩大到一般的单数指数序列,如二元形、Poisson 和 chi- square。 我们考虑对单质单质单质参数序列的估计,并根据经过修改的PAVA, 利用自然参数和预期参数的双重性, 开发一个高效的算法。 我们还提供了使用信息标准选择正规化参数的方法。 模拟结果显示, 拟议的方法以数据驱动的方式检测了单质单质单质参数序列的变化点。 还介绍了对光谱估计、 因果关系和 ODE 解算法的分解法的应用 。