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Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…

Methodology · Statistics 2025-09-16 Hongying Li , Minyi Zhu , Yaqi Cao , Xinyi Xu

Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not…

Machine Learning · Statistics 2021-03-04 Runxiong Wu , Xin Chen

We study the problem of robust estimation of the mean vector of a sub-Gaussian distribution. We introduce an estimator based on spectral dimension reduction (SDR) and establish a finite sample upper bound on its error that is…

Statistics Theory · Mathematics 2022-04-06 Amir-Hossein Bateni , Arshak Minasyan , Arnak S. Dalalyan

In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and…

Statistics Theory · Mathematics 2020-05-04 Emmanuel de Dieu Nkou , Guy Martial Nkiet

Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

Statistics Theory · Mathematics 2021-10-26 Efstathia Bura , Liliana Forzani , Rodrigo García Arancibia , Pamela Llop , Diego Tomassi

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…

Methodology · Statistics 2022-12-08 Qi Zhang , Lingzhou Xue , Bing Li

Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…

Numerical Analysis · Mathematics 2017-10-09 Andrew Glaws , Paul G. Constantine

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

Machine Learning · Statistics 2023-05-26 Aditya Ravuri , Francisco Vargas , Vidhi Lalchand , Neil D. Lawrence

In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…

Methodology · Statistics 2014-03-26 Luke A. Prendergast , Alexandra L. Garnham

We consider high dimensional $M$-estimation in settings where the response $Y$ is possibly missing at random and the covariates $\mathbf{X} \in \mathbb{R}^p$ can be high dimensional compared to the sample size $n$. The parameter of interest…

Methodology · Statistics 2019-11-27 Abhishek Chakrabortty , Jiarui Lu , T. Tony Cai , Hongzhe Li

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…

Statistics Theory · Mathematics 2007-06-13 Arnak Dalalyan , Anatoly Juditsky , Vladimir Spokoiny

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space…

Machine Learning · Computer Science 2014-08-15 Bing Li , Hongyuan Zha , Francesca Chiaromonte

Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…

Statistics Theory · Mathematics 2018-07-10 Emilie Devijver , Emeline Perthame

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations…

Statistics Theory · Mathematics 2012-03-16 Xiangrong Yin , Bing Li

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…

Machine Learning · Statistics 2013-11-07 Stoyan Georgiev , Sayan Mukherjee

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…

Methodology · Statistics 2023-03-09 Chanwoo Lee

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

Methodology · Statistics 2015-03-05 Silvia Bianconcini , Silvia Cagnone , Dimitris Rizopoulos

This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into multivariate statistical process monitoring. Provides an extension of SIR for the single-index model by adopting the idea from partial least…

Applications · Statistics 2012-02-03 Yue Yu , Zhijie Sun

A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically,…

Methodology · Statistics 2014-01-03 Tao Wang , Xu Guo , Peirong Xu , Lixing Zhu