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Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
A new way to design parameter estimators with enhanced performance is proposed in the paper. The procedure consists of two stages, first, the generation of new regression forms via the application of a dynamic operator to the original…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and…
We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…
This paper introduces a parameter adaptation-based control law for a class of nonlinear, control-affine, safety-critical systems subject to additive, parameter-affine model uncertainty. It is shown that the uncertainty is learned in…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…