Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression

Isotonic Regression by Dynamic Programming

Estimating a Bounded Normal Mean Under the LINEX Loss Function

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

Bayesian 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...

Optimal 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...

Risk Bounds in Isotonic Regression

Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform n−1/3-consistency of the p risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability d...