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In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is…

Methodology · Statistics 2014-12-01 Natalie Neumeyer , Hohsuk Noh , Ingrid Van Keilegom

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…

Statistics Theory · Mathematics 2010-10-20 Pang Du , Shuangge Ma , Hua Liang

We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…

Statistics Theory · Mathematics 2019-07-04 David Gamarnik , Julia Gaudio

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Statistics Theory · Mathematics 2021-02-12 Qiyang Han

We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…

Statistics Theory · Mathematics 2015-07-31 Sabyasachi Chatterjee , Adityanand Guntuboyina , Bodhisattva Sen

Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…

Statistics Theory · Mathematics 2017-04-25 Zhiqiang Tan , Cun-Hui Zhang

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Statistics Theory · Mathematics 2023-03-23 Reese Pathak , Martin J. Wainwright , Lin Xiao

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…

Statistics Theory · Mathematics 2021-01-01 Xiaoou Pan , Qiang Sun , Wen-Xin Zhou

Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…

Computer Vision and Pattern Recognition · Computer Science 2021-11-23 Jing Zhang , Yuchao Dai , Mehrtash Harandi , Yiran Zhong , Nick Barnes , Richard Hartley

This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The…

Statistics Theory · Mathematics 2011-02-23 Xavier Brossat , Georges Oppenheim , Marie-Claude Viano

This paper considers the problem of adaptive estimation of a template in a randomly shifted curve model. Using the Fourier transform of the data, we show that this problem can be transformed into a stochastic linear inverse problem. Our aim…

Statistics Theory · Mathematics 2009-11-10 Jérémie Bigot , Sébastien Gadat , Clément Marteau

We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible…

Machine Learning · Computer Science 2019-09-27 Miruna Oprescu , Vasilis Syrgkanis , Zhiwei Steven Wu

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

Statistics Theory · Mathematics 2020-07-07 Xiaowei Yang , Huiming Zhang , Haoyu Wei , Shouzheng Zhang

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…

Machine Learning · Statistics 2015-11-17 Zhuoran Yang , Zhaoran Wang , Han Liu , Yonina C. Eldar , Tong Zhang

We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities…

Statistics Theory · Mathematics 2016-01-05 Anders Bredahl Kock , Haihan Tang

In a general counting process setting, we consider the problem of obtaining a prognostic on the survival time adjusted on covariates in high-dimension. Towards this end, we construct an estimator of the whole conditional intensity. We…

Statistics Theory · Mathematics 2013-10-15 Sarah Lemler

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

Statistics Theory · Mathematics 2012-11-02 Jérémie Bigot , Theofanis Sapatinas

A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators…

Statistics Theory · Mathematics 2007-08-22 Irene Gijbels , Danyu Lin , Zhiliang Ying

We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…

Methodology · Statistics 2023-11-08 Conceição Amado , Ana M. Bianco , Graciela Boente , Isabel M. Rodrigues

Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we…

Statistics Theory · Mathematics 2013-07-09 A. Chatterjee , S. N. Lahiri