相关论文: Improving Point and Interval Estimates of Monotone…

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…

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.…

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and P\'olya as a sorting device for functions. Assuming that $x$ is a monotone function and that an estimate $x_n$ of $x$ is given, consider the monotone…

In this paper, the model $Y_i=g(Z_i),\ i=1,2,...,n$ with $Z_i$ being random variables with known distribution and $g(x)$ being unknown strictly increasing function is proposed and almost sure convergence of estimator for $g(x)$ is proved…

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the…

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment…

Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…

We consider a general collection of function classes on the interval $[0,1]$ defined in terms of certain averages and show that monotone rearrangement does not increase the class constant in each case. The formulation includes BMO and $A_2$…

We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a…

In many problems, a sensible estimator of a possibly multivariate monotone function may itself fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid…

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

This paper presents a unified rank-based inferential procedure for fitting the accelerated failure time model to partially interval-censored data. A Gehan-type monotone estimating function is constructed based on the idea of the familiar…

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…

In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…