AN EMPIRICAL DISTRIBUTION FUNCTION FOR SAMPLING WITH INCOMPLETE INFORMATION

By M. Ayer, H. D. Brunk, G. Ewing, W. T. Reid, E. Silverman. 1955

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Citations in the corpus

Generalized Sparse Additive Models (2019, methodology): “…and Tibshirani, 2015]; with the convex indicator of an M -dimensional linear subspace, (13) can be solved in O ( M 2 n ) operations using linear regression; using a monotonicity indicator, (13) can be solved with the pool adjacent violators algorithm in O ( n ) operations [Ayer et al., 1955].”
Differentially-private network trace analysis (2010, background): “, the “pool adjacent violators” algorithm [3]) can find the non-decreasing curve that minimizes the squared error distance from the input.”
Nonparametric Shape-Restricted Regression (2017, background): “ ng; (4) which is a closed convex cone in Rn (Iis dened through n 1 linear constraints). The above problem is typically known as isotonic regression and has a long history in statistics; see e.g., [23,5,138]. Example 1.2 (Order preserving regression on a partially ordered set). Isotonic regression c”
Are Tourists Really Willing to Pay More for Sustainable Destinations (2016, background): “[90] as an extreme case of double censoring.”
Predicting tree mortality from diameter growth : a comparison of maximum likelihood and Bayesian approaches (2000, methodology): “To evaluate our parametric estimates we compare a nonparametric model that is constrained only by the assumption that risk changes monotonically with growth rate (Ayer et al. 1955).”
Multidimensional Scaling Using Majorization: SMACOF in R (2008, methodology): “In MDS literature this problem is referred to as primary monotone least squares regression and smacof solves it by means of the pooledadjacent-violators algorithm (PAVA, Ayer, Brunk, Ewing, Reid, and Silverman 1955; Barlow, Bartholomew, Bremner, and Brunk 1972).”
The Worth of a Possum: Valuing Species with the Contingent Valuation Method (2001, methodology): “Because the observed yes proportions do not follow a consistent decline as the bid amount increases, it was necessary to ‘smooth’ the estimates using the method developed by Ayer et al. (1955) to get a monotonic sequence.”
Additive Isotonic Models (1989, methodology): “The CPAV algorithm for fitting additive isotonic models combines the overall cyclic process used in fitting other nonparametric additive models (Hastie and Tibshirani 1986a) with a violator-pooling strategy (Ayer et al. 1955) for finding the optimal isotonic transformation at each step with all of t”
Optimal rates of statistical seriation (2016, methodology): “The LS estimator defined by θ̂ = argminθ∈Sn ‖θ− y‖ 2 2 can be computed in closed form in O(n) using the Pool-Adjacent-Violators algorithm (PAVA) [6, 8, 59] and its statistical performance has been studied by Zhang [72] (see also [57, 30, 68, 53, 70] for similar bounds using empirical process theory)”
Likelihood Ratio Tests for Monotone Functions (2001, background): “to make inference about the monotone (increasing) function F. The nonparametric maximum likelihood estimator n of F is well known; see, for example, Ayer, Brunk, Ewing, Reid and Silverman (1955) or Groeneboom and Wellner (1992).”