The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a better approximation to that function.In this paper, we consider the formulation which assumes that the data were generated by a continuous monotonic function obeying the Lipschitz condition. We propose a new algorithm, the Lipschitz pool adjacent violators (LPAV) algorithm, which approximates that function; we prove the convergence of the algorithm and examine its complexity.

中文翻译：

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Lipschitz 约束下的等张回归


池相邻违规者 (PAV) 算法是解决具有完全排序的等渗回归问题类的有效技术。该算法产生逐步等渗估计，该估计近似函数并将最大似然分配给数据。然而，如果有理由相信数据是由连续函数生成的，则更平滑的估计可能会为该函数提供更好的近似值。在本文中，我们考虑假设数据是由连续单调函数生成的公式服从利普希茨条件。我们提出了一种新算法，即 Lipschitz 池相邻违规者 (LPAV) 算法，该算法近似该函数；我们证明了算法的收敛性并检验了其复杂性。