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Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Adaptively collected data has become ubiquitous within modern practice. However, even seemingly benign adaptive sampling schemes can introduce severe biases, rendering traditional statistical inference tools inapplicable. This can be…

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to…

We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…

We consider the problem of variables selection and estimation in linear regression model in situations where the number of parameters diverges with the sample size. We propose the adaptive Generalized Ridge-Lasso (\mbox{AdaGril}) which is…

In this paper for the first time the nonparametric autoregression estimation problem for the quadratic risks is considered. To this end we develop a new adaptive sequential model selection method based on the efficient sequential kernel…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world…

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and…

This paper investigates the problem of selecting variables in regression-type models for an "instrumental" setting. Our study is motivated by empirically verifying the conditional convergence hypothesis used in the economical literature…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these…

Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…