Related papers: Iterative Isotonic Regression
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
Isotonic distributional regression (IDR) is a powerful nonparametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and…
Isotonic regression (IR) is shape-constrained regression to maintain a univariate fitting curve non-decreasing, which has numerous applications including single-index models and probability calibration. When it comes to multi-output…
Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting…
Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…
Univariate isotonic regression (IR) has been used for nonparametric estimation in dose-response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the…
We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…
Isotonic regression is a shape-constrained nonparametric regression in which the regression is an increasing step function. For $n$ data points, the number of steps in the isotonic regression may be as large as $n$. As a result, standard…
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…
This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a…
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.…
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…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…
We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…
The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that…
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…