Related papers: Error estimation and adaptive tuning for unregular…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $\epsilon$.…

The sample selection approach is very popular in learning with noisy labels. As deep networks learn pattern first, prior methods built on sample selection share a similar training procedure: the small-loss examples can be regarded as clean…

Standard local polynomial estimators of a nonparametric regression function employ a weighted least squares loss function that is tailored to the setting of homoscedastic Gaussian errors. We introduce the outrigger local polynomial…

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…

Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…

This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L_1-risk of the estimator is given. The method is applied to the shape respecting…

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…

We study asymptotic properties of $M$-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the $M$-estimates are derived and a central limit theorem is established.…

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character…

In this paper, we propose a robust profile estimation method for the parametric and nonparametric components of a single index model when the errors have a strongly unimodal density with unknown nuisance parameter. Under regularity…

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…

We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…