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This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback penalty is a weakly convex function. It bears various…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This…
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…