منابع مشابه
Isotonic Median Regression via Scaling
This paper gives algorithms for determining isotonic median regressions (i.e., isotonic regression using the L1 metric) satisfying order constraints given by various ordered sets. For a rooted tree the regression can be found in Θ(n log n) time, while for a star it can be found in Θ(n) time, where n is the number of vertices. For bivariate data, when the set is a grid the regression can be foun...
متن کاملInference for Multiple Isotonic Regression
The isotonic regression for two or more independent variables is a classic problem in data analysis. The classical solution involves enumeration of upper sets, which is computationally prohibitive unless the sample size is small. Here it is shown that the solution may be obtained through a single projection onto a convex polyhedral cone. The cone formulation allows an exact test of the null hyp...
متن کاملBayesian isotonic density regression.
Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not c...
متن کاملOptimal Reduced Isotonic Regression
Isotonic regression is a shape-constrained nonparametric regression in which the ordinate is a nondecreasing function of the abscissa. The regression outcome is an increasing step function. For an initial set of n points, the number of steps in the isotonic regression, m, may be as large as n. As a result, the full isotonic regression has been criticized as overfitting the data or making the re...
متن کاملOnline Isotonic Regression
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total squared loss compared against the best isotonic (nondecreasing) function in hindsight. We survey several standard online learning algorithms and show that n...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1973
ISSN: 0090-5364
DOI: 10.1214/aos/1176342408