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A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…

Statistics Theory · Mathematics 2015-12-01 Sourav Chatterjee

To what extent can agents with misspecified subjective models predict false correlations? We study an "analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst fits each equation to…

Theoretical Economics · Economics 2019-11-05 Kfir Eliaz , Ran Spiegler , Yair Weiss

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

Statistics Theory · Mathematics 2020-09-17 Peggy Cénac , Antoine Godichon-Baggioni , Bruno Portier

We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex…

Machine Learning · Computer Science 2023-04-03 Kaan Gokcesu , Hakan Gokcesu

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

Methodology · Statistics 2021-05-17 Peng Tang , Huijing Jiang , Heeyoung Kim , Xinwei Deng

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

Machine Learning · Statistics 2015-05-14 Xinyang Yi , Zhaoran Wang , Constantine Caramanis , Han Liu

Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…

Methodology · Statistics 2017-05-17 James P. Long

In all applications in digital communications, it is crucial for an estimator to be unbiased. Although so-called soft feedback is widely employed in many different fields of engineering, typically the biased estimate is used. In this paper,…

Information Theory · Computer Science 2018-02-21 Susanne Sparrer , Robert F. H. Fischer

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…

Statistics Theory · Mathematics 2007-06-13 Florentina Bunea

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…

Methodology · Statistics 2022-10-11 Katarzyna Reluga , Ting Ye , Qingyuan Zhao

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

Information Theory · Computer Science 2017-04-05 Abbas Kazemipour , Sina Miran , Piya Pal , Behtash Babadi , Min Wu

In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…

Methodology · Statistics 2020-05-15 Beste Hamiye Beyaztas , Soutir Bandyopadhyay

This paper presents an integrated framework for estimation and inference from generalized linear models using adjusted score equations that result in mean and median bias reduction. The framework unifies theoretical and methodological…

Methodology · Statistics 2019-01-15 Ioannis Kosmidis , Euloge Clovis Kenne Pagui , Nicola Sartori

Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…

Computational Engineering, Finance, and Science · Computer Science 2018-04-17 C. P. E. Agbachi

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…

Machine Learning · Computer Science 2024-02-22 Gavin Brown , Krishnamurthy Dvijotham , Georgina Evans , Daogao Liu , Adam Smith , Abhradeep Thakurta

Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…

Machine Learning · Statistics 2018-04-12 Damian Kozbur

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Methodology · Statistics 2025-02-07 Neil K. Chada , Ajay Jasra , Mohamed Maama , Raul Tempone

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…

Statistics Theory · Mathematics 2014-11-21 Sourav Chatterjee

In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…

Statistics Theory · Mathematics 2022-06-28 Julien Chhor , Suzanne Sigalla , Alexandre B. Tsybakov

We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…

Methodology · Statistics 2015-07-17 Aaron J. Molstad , Adam J. Rothman