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This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

Statistics Theory · Mathematics 2025-08-06 Yichen Lyu , Pengkun Yang

Existing high-dimensional statistical methods are largely established for analyzing individual-level data. In this work, we study estimation and inference for high-dimensional linear models where we only observe "proxy data", which include…

Methodology · Statistics 2022-01-12 Sai Li , T. Tony Cai , Hongzhe Li

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…

Methodology · Statistics 2020-07-01 Guorong Dai , Ursula U. Müller , Raymond J. Carroll

Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as $g(<a,x>)$, where a is an unknown index vector and x are the features. This…

Statistics Theory · Mathematics 2020-12-08 Zeljko Kereta , Timo Klock , Valeriya Naumova

In this letter, we consider the problem of detecting a high dimensional signal based on compressed measurements with physical layer secrecy guarantees. We assume that the network operates in the presence of an eavesdropper who intends to…

Information Theory · Computer Science 2015-06-02 Bhavya Kailkhura , Sijia Liu , Thakshila Wimalajeewa , Pramod K. Varshney

We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…

Statistics Theory · Mathematics 2019-03-05 Li Jialiang , Lv Jing

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…

Statistics Theory · Mathematics 2015-03-19 Po-Ling Loh , Martin J. Wainwright

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units…

Statistics Theory · Mathematics 2024-01-10 Edgar Dobriban , Weijie J. Su , Yachong Yang , Zhixiang Zhang

Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…

Machine Learning · Statistics 2015-07-01 Ravi Ganti , Nikhil Rao , Rebecca M. Willett , Robert Nowak

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

Methodology · Statistics 2024-04-09 Shijie Cui , Xu Guo , Zhe Zhang

We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…

Methodology · Statistics 2023-03-21 Siyi Deng , Yang Ning , Jiwei Zhao , Heping Zhang

We present a mathematically justifiable, computationally simple, sample eigenvalue based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a…

Statistics Theory · Mathematics 2007-05-23 N. Raj Rao , Alan Edelman

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…

Statistics Theory · Mathematics 2014-06-24 Sara van de Geer , Peter Bühlmann , Ya'acov Ritov , Ruben Dezeure

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…

Information Theory · Computer Science 2016-11-15 Pascal Vallet , Philippe Loubaton , Xavier Mestre

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

Machine Learning · Statistics 2015-03-19 Tianqi Zhao , Mladen Kolar , Han Liu

In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the…

Methodology · Statistics 2009-05-14 Jane-Ling Wang , Liugen Xue , Lixing Zhu , Yun Sam Chong

We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…

Statistics Theory · Mathematics 2019-04-12 Anatoli Juditsky , Arkadi Nemirovski

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…

Statistics Theory · Mathematics 2010-02-25 Jim Kuelbs , Anand N. Vidyashankar

We consider the linearly transformed spiked model, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: \begin{align*} Y_i = A_i X_i + \varepsilon_i, \end{align*} for $i=1,\ldots,n$. The transform…

Statistics Theory · Mathematics 2018-07-13 Edgar Dobriban , William Leeb , Amit Singer