Related papers: Model-Estimation-Free, Dense, and High Dimensional…

In this paper, we provide a novel Model-free approach based on Deep Neural Network (DNN) to accomplish point prediction and prediction interval under a general regression setting. Usually, people rely on parametric or non-parametric models…

We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…

We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…

When multiple models are considered in regression problems, the model averaging method can be used to weigh and integrate the models. In the present study, we examined how the goodness-of-prediction of the estimator depends on the…

This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regression is a…

A new type of robust estimation problem is introduced where the goal is to recover a statistical model that has been corrupted after it has been estimated from data. Methods are proposed for "repairing" the model using only the design and…

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

The task of modeling claim severities is addressed when data is not consistent with the classical regression assumptions. This framework is common in several lines of business within insurance and reinsurance, where catastrophic losses or…

Estimation of the density of regression errors is a fundamental issue in regression analysis and it is typically explored via a parametric approach. This article uses a nonparametric approach with the mean integrated squared error (MISE)…

In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…

Mixture models are well-established learning approaches that, in computer vision, have mostly been applied to inverse or ill-defined problems. However, they are general-purpose divide-and-conquer techniques, splitting the input space into…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…

We consider a problem of linear model selection in the presence of both continuous and categorical predictors. Feasible models consist of subsets of numerical variables and partitions of levels of factors. A new algorithm called delete or…

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and…