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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…

Statistics Theory · Mathematics 2008-12-18 Ou Zhao , Michael Woodroofe

In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…

Statistics Theory · Mathematics 2026-01-23 Omar Al-Ghattas

In high-dimensional data settings where $p\gg n$, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable…

Methodology · Statistics 2016-03-24 Xiaoli Gao , S. E. Ahmed , Yang Feng

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

Methodology · Statistics 2024-03-11 Ryan Thompson , Farshid Vahid

Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…

Econometrics · Economics 2019-05-28 Xinwei Ma , Jingshen Wang

We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…

Statistics Theory · Mathematics 2016-09-29 Pierre C. Bellec

We consider the problem of combining data from observational and experimental sources to make causal conclusions. This problem is increasingly relevant, as the modern era has yielded passive collection of massive observational datasets in…

Methodology · Statistics 2020-05-19 Evan Rosenman , Guillaume Basse , Art Owen , Michael Baiocchi

We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…

Statistics Theory · Mathematics 2020-05-25 Masoud M Nasari , Mohamedou Ould-Haye

Estimating the probabilistic Worst-Case Execution Time (pWCET) is essential for ensuring the timing correctness of real-time applications, such as in robot IoT systems and autonomous driving systems. While methods based on Extreme Value…

Machine Learning · Statistics 2025-11-18 Hayate Toba , Atsushi Yano , Takuya Azumi

This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…

Statistics Theory · Mathematics 2025-12-03 Octavio César Mesner

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…

Methodology · Statistics 2015-05-08 Zhuang Ma , Dean Foster , Robert Stine

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

Machine Learning · Statistics 2019-11-05 Song Liu , Takafumi Kanamori , Wittawat Jitkrittum , Yu Chen

Let $X$ be a random vector with distribution $P_{\theta}$ where $\theta$ is an unknown parameter. When estimating $\theta$ by some estimator $\varphi(X)$ under a loss function $L(\theta,\varphi)$, classical decision theory advocates that…

Methodology · Statistics 2012-03-23 Dominique Fourdrinier , Martin T. Wells

We consider estimation and inference in a single index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least squares estimator (CLSE) for both the parametric and the nonparametric…

Statistics Theory · Mathematics 2021-01-15 Arun K. Kuchibhotla , Rohit K. Patra , Bodhisattva Sen

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional…

Applications · Statistics 2022-10-04 Timothy B. Armstrong , Michal Kolesár

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

Methodology · Statistics 2016-05-03 Juhee Cho , Donggyu Kim , Karl Rohe

In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations,…

Methodology · Statistics 2011-08-08 Peng Lai , Qihua Wang , Heng Lian

Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…

Machine Learning · Statistics 2023-08-03 Meng Qi , Paul Grigas , Zuo-Jun Max Shen

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Econometrics · Economics 2021-12-23 Dimitris Korobilis , Kenichi Shimizu

The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent…

Applications · Statistics 2020-02-19 Daniel B. Williamson , Philip G. Sansom