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We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Probability · Mathematics 2017-11-28 Andrew Papanicolaou , Konstantinos Spiliopoulos

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…

Statistics Theory · Mathematics 2017-10-16 Jana Jankova , Sara van de Geer

Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…

Machine Learning · Computer Science 2024-03-04 Xiaoxin Yin , David S. Yin

The family of rank estimators, including Han's maximum rank correlation (Han, 1987) as a notable example, has been widely exploited in studying regression problems. For these estimators, although the linear index is introduced for…

Statistics Theory · Mathematics 2019-08-15 Yanqin Fan , Fang Han , Wei Li , Xiao-Hua Zhou

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…

Statistics Theory · Mathematics 2014-05-06 Piero Barone , Isabella Lari

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

Statistics Theory · Mathematics 2017-01-23 Yannick Baraud , Lucien Birgé , Mathieu Sart

Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In…

Statistics Theory · Mathematics 2015-07-14 Itai Dattner , Chris A. J. Klaassen

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

Machine Learning · Statistics 2020-03-04 Michael Celentano , Andrea Montanari , Yuchen Wu

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…

Econometrics · Economics 2023-02-14 Abhishek K. Umrawal , Joshua C. C. Chan

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

Machine Learning · Computer Science 2023-10-26 Tsai Hor Chan , Kin Wai Lau , Jiajun Shen , Guosheng Yin , Lequan Yu

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

Methodology · Statistics 2013-09-24 Zuofeng Shang , Ping Li

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

Systems and Control · Computer Science 2016-04-08 Ortega Romeo , Bobtsov Alexey , Pyrkin Anton , Aranovskiy Stanislav

In this paper, we investigate the parameter estimation problem for reflected OU processes. Both the estimates based on continuously observed processes and discretely observed processes are considered. The explicit formulas for the…

Methodology · Statistics 2022-05-03 Han Yuecai , Zhang Dingwen

A fundamental challenge in semi-supervised learning lies in the observed data's disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing…

Methodology · Statistics 2026-05-12 Yuqian Zhang , Jelena Bradic

This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…

Methodology · Statistics 2020-06-09 M. Taavoni , M. Arashi

Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $\psi$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous…

Statistics Theory · Mathematics 2026-01-27 Lin Liu , Rajarshi Mukherjee , Whitney K. Newey , James M. Robins

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Probability · Mathematics 2021-04-13 Suryadeepto Nag

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…

Machine Learning · Statistics 2015-01-28 Zhaoran Wang , Quanquan Gu , Yang Ning , Han Liu

Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…

Probability · Mathematics 2016-05-20 Yaniv Plan , Roman Vershynin , Elena Yudovina