170 citations · 1k across the 48 of their papers we have counts for
48 papers · 1 filter
Bi--Concave Distributions
Nilanjana Laha, Zhen Miao, Jon A. Wellner
We introduce new shape-constrained classes of distribution functions on R, the bi--concave classes. In parallel to results of Dümbgen, Kolesnyk, and Wilke (2017) for what they…
The density ratio of Poisson binomial versus Poisson distributions
Lutz Duembgen, Jon A. Wellner
Let be the probability that a sum of independent Bernoulli random variables with parameters equals , where $λ:= p_1 + p_2 + p_3 + \cdots…
Complex sampling designs: uniform limit theorems and applications
Qiyang Han, Jon A. Wellner
In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Gl…
Bounding distributional errors via density ratios
Lutz Duembgen, Richard Samworth, Jon Wellner
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution to…
Robustness of shape-restricted regression estimators: an envelope perspective
Qiyang Han, Jon A. Wellner
Classical least squares estimators are well-known to be robust with respect to moment assumptions concerning the error distribution in a wide variety of finite-dimensional statisti…
Estimation of mean residual life
W. J. Hall, Jon A. Wellner
Yang (1978) considered an empirical estimate of the mean residual life function on a fixed finite interval. She proved it to be strongly uniformly consistent and (when appropriatel…
Efron's monotonicity property for measures on
Adrien Saumard, Jon A. Wellner
First we prove some kernel representations for the covariance of two functions taken on the same random variable and deduce kernel representations for some functionals of a continu…
Convergence rates of least squares regression estimators with heavy-tailed errors
Qiyang Han, Jon A. Wellner
We study the performance of the Least Squares Estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a …
Bi--concave distributions
Nilanjana Laha, Jon A. Wellner
We introduce a new shape-constrained class of distribution functions on R, the bi--concave class. In parallel to results of Dümbgen, Kolesnyk, and Wilke (2017) for what they c…
The Bennett-Orlicz norm
Jon A. Wellner
Lederer and van de Geer (2013) introduced a new Orlicz norm, the Bernstein-Orlicz norm, which is connected to Bernstein type inequalities. Here we introduce another Orlicz norm, th…
Univariate log-concave density estimation with symmetry or modal constraints
Charles R. Doss, Jon A. Wellner
We study nonparametric maximum likelihood estimation of a log-concave density function which is known to satisfy further constraints, where either (a) the mode of i…
Multivariate convex regression: global risk bounds and adaptation
Qiyang Han, Jon A. Wellner
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of converg…
Exponential bounds for the hypergeometric distribution
Evan Greene, Jon A. Wellner
We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distri…
Approximation and Estimation of s-Concave Densities via Rényi Divergences
Qiyang Han, Jon A. Wellner
In this paper, we study the approximation and estimation of -concave densities via Rényi divergence. We first show that the approximation of a probability measure by an -…
Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics
Evan Greene, Jon A. Wellner
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate s…
A law of the iterated logarithm for Grenander's estimator
Lutz Duembgen, Jon A. Wellner, Malcolm Wolff
In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If , , and is continuo…
On Convex Least Squares Estimation when the Truth is Linear
Yining Chen, Jon A. Wellner
We prove that the convex least squares estimator (LSE) attains a pointwise rate of convergence in any region where the truth is linear. In addition, the asymptotic distr…
Log-concavity and strong log-concavity: a review
Adrien Saumard, Jon A. Wellner
We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly l…
A New Approach to Tests and Confidence Bands for Distribution Functions
Lutz Duembgen, Jon A. Wellner
We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multi-scale methods of testing and based on refined laws…
Global Rates of Convergence of the MLEs of Log-concave and s-concave Densities
Charles R. Doss, Jon A. Wellner
We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and -concave densities on . The main finding is that the rate of…
On the Hermite spline conjecture and its connection to k-monotone densities
Fadoua Balabdaoui, Simon Foucart, Jon A. Wellner
The k-monotone classes of densities defined on (0, \infty) have been known in the mathematical literature but were for the first time considered from a statistical point of view by…
Global Rates of Convergence of the MLE for Multivariate Interval Censoring
Jon A. Wellner, Fuchang Gao
We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function in the case of (one type of) "interval censored" data. Th…
A general semiparametric Z-estimation approach for case-cohort studies
Bin Nan, Jon A. Wellner
Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-co…
Chernoff's density is log-concave
Fadoua Balabdaoui, Jon A. Wellner
We show that the density of , sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strong…