Related papers: Grenander--Stone estimator: stacked constrained es…

In this paper we consider the stacking of isotonic regression and the method of rearrangement with the empirical estimator to estimate a discrete distribution with an infinite support. The estimators are proved to be strongly consistent…

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…

Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's…

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…

The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development…

The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…

Westling and Carone (2020) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution…

The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive…

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…

In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained…

We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…

In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk's classical isotonic estimator. We also…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…

It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…

A new model validation and performance assessment tool is introduced, the sliding threshold of observation for numeric evaluation (STONE) curve. It is based on the relative operating characteristic (ROC) curve technique, but instead of…

We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include…

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…

We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…