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Wednesday, 4 November 2026: 0 new papers, 2 cross-lists and 2 replacements in Other Statistics (stat.OT), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
In this paper we study a regularized version of nearly-isotonic regression with respect to a general partial order. In this estimator the sum of squares is weighted, with some of the weights allowed to be zero, and an additional quadratic penalty is imposed. The only assumption we make is that the quadratic part of the objective function is strictly convex, and we show that this assumption is mild. First, we show that for all sufficiently large values of the penalty parameter the estimator coincides with the regularized isotonic regression, in which the penalty is replaced by the isotonic constraint. Further, we prove that the resulting problem can be written as a generalized lasso problem with a design matrix of full column rank and with the penalty matrix unchanged. Next, we derive the dual problem, which is a quadratic program with box constraints, and write it in a sparse form that can be solved by standard quadratic programming solvers for sparse problems.
A system contains an unknown number $N$ of units, each failing at an unknown common rate, each unit is removed once it fails. The failure-rate declines as units are removed, but after only a few failures the decline is too slight to distinguish from a constant rate, and the maximum-likelihood estimate of $N$ is infinite with substantial probability. This is a well-known feature of the model, but its probability has not been quantified. We show that about $N^{2/3}$ failures are needed before a finite population can be distinguished from an inexhaustible one, and that at this scale the profile log-likelihood ratio converges to that of a Gaussian shift experiment, in which an infinite estimate occurs with a calculable probability. The exponent is not a property of the model alone. Profiling annihilates the Taylor terms that the nuisance-parameters can reproduce, and detectability is governed by the first surviving term. For example, unknown drift in testing-effort reproduces the linear term, leaving a quadratic survivor and raising the requirement to $N^{4/5}$; in general the critical scale is $N^{2q/(2q+1)}$ for a survivor of order $q$. We obtain the limiting-law of the estimator, the null likelihood ratio distribution, and confidence sets that may be unbounded.