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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 consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…

Statistics Theory · Mathematics 2013-02-04 Shujie Ma , Qiongxia Song , Li Wang

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Machine Learning · Statistics 2012-06-22 Tingni Sun , Cun-Hui Zhang

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

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

Statistics Theory · Mathematics 2017-05-29 Forzani Liliana , Fraiman Ricardo , Llop Pamela

Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…

Statistics Theory · Mathematics 2015-10-19 Ezequiel Smucler , Víctor J. Yohai

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 Takumi Kawashima , Qing Yu , Akari Asai , Daiki Ikami , Kiyoharu Aizawa

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…

Statistics Theory · Mathematics 2011-03-09 Bo Kai , Runze Li , Hui Zou

We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…

Statistics Theory · Mathematics 2013-11-21 Lan Wang , Yongdai Kim , Runze Li

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation…

We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…

Statistics Theory · Mathematics 2016-07-07 Clément Levrard

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

This is the second part of the research project initiated in Cleanthous et al (2024). We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent…

Statistics Theory · Mathematics 2024-05-28 Galatia Cleanthous , Athanasios G. Georgiadis , Oleg V. Lepski

We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…

Methodology · Statistics 2014-05-27 Alexandre Belloni , Victor Chernozhukov , Lie Wang

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

Statistics Theory · Mathematics 2025-02-27 Marie-Christine Düker , Adam Waterbury

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

In this work, we present the misspecified Gaussian Cram\'er-Rao lower bound for the parameters of a harmonic signal, or pitch, when signal measurements are collected from an almost, but not quite, harmonic model. For the asymptotic case of…

Signal Processing · Electrical Eng. & Systems 2019-10-29 Filip Elvander , Jie Ding , Andreas Jakobsson

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

This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for…

Methodology · Statistics 2022-02-08 Shaomin Li , Haoyu Wei , Xiaoyu Lei

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…

Statistics Theory · Mathematics 2014-01-14 Hanzhong Liu , Bin Yu