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This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…

Methodology · Statistics 2016-12-06 Tianqing Liu , Xiaohui Yuan , Zhaohai Li , Aiyi Liu

We study reconstruction operators on a Hilbert space that are exact on a given reconstruction subspace. Among those the reconstruction operator obtained by the least squares fit has the smallest operator norm, and therefore is most stable…

Numerical Analysis · Mathematics 2019-09-18 Peter Berger , Karlheinz Gröchenig , Gerald Matz

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best…

Optimization and Control · Mathematics 2017-07-25 Peyman Mohajerin Esfahani , Soroosh Shafieezadeh-Abadeh , Grani Adiwena Hanasusanto , Daniel Kuhn

We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel…

Statistics Theory · Mathematics 2023-05-10 Timo Dimitriadis , Tobias Fissler , Johanna Ziegel

In this work, we propose a deep neural network method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. By properly choosing…

Machine Learning · Statistics 2020-12-09 Shuoyang Wang , Guanqun Cao , Zuofeng Shang

We study the problem of nonparametric estimation of a multivariate function $g:\mathbb {R}^d\to\mathbb{R}$ that can be represented as a composition of two unknown smooth functions $f:\mathbb{R}\to\mathbb{R}$ and $G:\mathbb{R}^d\to…

Statistics Theory · Mathematics 2009-06-05 Anatoli B. Juditsky , Oleg V. Lepski , Alexandre B. Tsybakov

Since polynomial regression models are generally quite reliable for data with a linear trend, it is important to note that, in some cases, they may encounter overfitting issues during the training phase, which could result in negative…

Methodology · Statistics 2025-03-21 Anthony Torres-Hernandez

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…

Statistics Theory · Mathematics 2015-01-05 Po-Ling Loh , Martin J. Wainwright

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…

Optimization and Control · Mathematics 2011-10-13 Zachary T. Harmany , Roummel F. Marcia , Rebecca M. Willett

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…

Statistics Theory · Mathematics 2019-06-13 Djihad Benelmadani , Karim Benhenni , Sana Louhichi

We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…

Statistics Theory · Mathematics 2009-02-13 Christoph Breunig , Jan Johannes

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

Statistics Theory · Mathematics 2009-09-29 Jérémie Bigot , Rolando Biscay , Jean-Michel Loubes , Lilian Muniz Alvarez

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input…

Graphics · Computer Science 2019-08-29 Ruqi Huang , Marie-Julie Rakotosaona , Panos Achlioptas , Leonidas Guibas , Maks Ovsjanikov

We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…

Complex Variables · Mathematics 2022-05-30 Ovidiu Costin , Gerald V. Dunne

We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…

Optimization and Control · Mathematics 2019-10-23 Jinming Xu , Ying Sun , Ye Tian , Gesualdo Scutari

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

Dynamical Systems · Mathematics 2023-11-01 Jason J. Bramburger , Giovanni Fantuzzi

We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what…

Methodology · Statistics 2022-12-26 Daniel Malinsky , Ilya Shpitser , Eric J Tchetgen Tchetgen

Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The…

Statistics Theory · Mathematics 2018-11-16 Johannes T. N. Krebs , Jürgen E. Franke

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Methodology · Statistics 2025-06-12 Tongyu Li , Fang Yao , Anru R. Zhang

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…

Statistics Theory · Mathematics 2024-01-22 Tapio Helin