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We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

We study the performance of the Least Squares Estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a $p$-th moment ($p\geq 1$). In such a heavy-tailed regression…

Several techniques exist to assess and reduce nonresponse bias, including propensity models, calibration methods, or post-stratification. These approaches can only be applied after the data collection, and assume reliable information…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small…

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…

When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most…

Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…

The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for…

This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and…

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression…

Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine…

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and…

Regression with a spherical response is challenging due to the absence of linear structure, making standard regression models inadequate. Existing methods, mainly parametric, lack the flexibility to capture the complex relationship induced…

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck.…

Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…