Related papers: Optimal monotone conditional error functions

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…

Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…

Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty. Designs with adaptive sample size need to account for their optional stopping to guarantee strict type-I…

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…

We will consider the damped Newton method for strongly monotone and Lipschitz continuous operator equations in a variational setting. We will provide a very accessible justification why the undamped Newton method performs better than its…

In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides…

This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score…

We consider an experiment with at least two stages or batches and $O(N)$ subjects per batch. First, we propose a semiparametric treatment effect estimator that efficiently pools information across the batches, and show it asymptotically…

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where…

We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…

We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…

In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is…

Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…

This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…