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High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
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…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
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…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
The asymptotic optimality (a.o.) of various hyper-parameter estimators with different optimality criteria has been studied in the literature for regularized least squares regression problems. The estimators include e.g., the maximum…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Threshold autoregressive moving-average (TARMA) models are popular in time series analysis due to their ability to parsimoniously describe several complex dynamical features. However, neither theory nor estimation methods are currently…
We study online transfer reinforcement learning (RL) in episodic Markov decision processes, where experience from related source tasks is available during learning on a target task. A fundamental difficulty is that task similarity is…
The objective of this paper is to extend an estimation method of parameters of the stable distributions in $\rd$ to the regularly varying tails distributions in an arbitrary cone. The consistency and the asymptotic normality of estimators…
Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…
Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…
In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…