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This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation…

This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|\beta_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge…

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…

A new modification of the minimum-contrast estimator (the weighted MCE) of drift parameter in a linear stochastic evolution equation with additive fractional noise is introduced in the setting of the spectral approach (Fourier coordinates…

Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by…

We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…

We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…

In this paper, we analyse the recovery properties of nonconvex regularized $M$-estimators, under the assumption that the true parameter is of soft sparsity. In the statistical aspect, we establish the recovery bound for any stationary point…

This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…

In this paper, we study the minimizers of U-processes and their domains of attraction. U-processes arise in various statistical contexts, particularly in M-estimation, where estimators are defined as minimizers of certain objective…

Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a…

A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…

Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…

Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…