Minimax Rates of ℓp-Losses for High-Dimensional Linear Errors-in-Variables Models over ℓq-Balls

Li, Xin; Wu, Dongya

doi:10.3390/e23060722

Cited by 4 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nghiem and Potgieter [75] introduced a new estimation method called simulation-selection-extrapolation (SIMSE-LEX), which used Lasso in the simulation step and group Lasso in the selection step. Li and Wu [76] established minimax convergence rates for the estimation of regression coefficients under a more general situation. Bai et al [77] proposed a variable selection method for ultrahigh-dimensional linear quantile regression models with measurement errors.…”

Section: Introductionmentioning

confidence: 99%

Overview of High-Dimensional Measurement Error Regression Models

Luo

Yue

2023

Mathematics

View full text Add to dashboard Cite

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained momentum due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of the objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several novel statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring in future research.

show abstract

Section: Introductionmentioning

confidence: 99%

Overview of High-Dimensional Measurement Error Regression Models

Luo

Yue

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Recently, researchers began to devote to errors-in-variables regression problems and most of the results were established for statistical inference of linear or generalized linear regression; see, e.g., [17][18][19][20] and references therein. In the information-theoretic aspect, Loh and Wainwright [21] and Li and Wu [22] considered linear errors-in-variables regression and established the minimax lower bound for estimating a sparse vector via calculating the corresponding KL divergence over certain sparse sets for vectors, respectively.…”

Section: Introductionmentioning

confidence: 99%

Minimax Lower Bounds for High-Dimensional Multi-Response Errors-in-Variables Regression

Li¹,

Wu²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Noisy data is always encountered in real applications, such as bioinformatics, neuroimage and remote sensing. Existing methods mainly consider linear or generalized linear errors-in-variables regression, while relatively little attention is paid for the multivariate response case, and how to evaluate the estimation performance under perturbed covariates is still an open question. In this paper, we consider the information-theoretic limitations of estimating a low-rank matrix in the multi-response errors-in-variables regression model. By application of the information theory and statistical techniques on concentration inequalities, the minimax lower bound is provided in terms of the squared Frobenius loss, which recaptures the rate provided under the clean covariate assumption in previous literatures. Hence our result further indicates that though under the more realistic errors-in-variables situation, no more samples are required so as to achieve a rate-optimal estimation.

show abstract

When should we use top coding in locally private estimation?

Ono,

Minami,

Hino

2024

Int. J. Inf. Secur.

View full text Add to dashboard Cite

Local differential privacy is a strict definition used to protect respondents in a distributed statistical survey against an untrusted survey organizer. Respondents randomize their records to make distinguishing any pair of records not easy in the system model, and LDP represents the easiness with a non-negative scalar . However, satisfying the requirements for larger record domains with a small can be challenging. One solution is top coding, which censors records that exceed a given threshold. Top coding reduces the range of the data and makes it easier to satisfy the requirements; however, top coding can also undermine the records' utility because it also reduces the information contained in the records. In this study, we attempted to determine when top coding effectively balances the privacy and the performance of estimators in LDP statistical estimations by analyzing the minimax risk, which measures the difficulty of an estimation problem. We classified estimation problems into three classes, characterizing them with the structure of the statistics and prior knowledge about the candidate populations, and derived the upper and lower bounds of minimax risks for them. The bounds suggest that (i) in the first class, the minimax risk can be arbitrarily large; (ii) in the second class, the minimax risk can always be small; and (iii) in the third class, only a moderate-size threshold gives a small minimax risk. Our findings suggest that practitioners should choose the statistic and threshold carefully and collect prior knowledge about the population to estimate the statistic with a small estimation error. KeywordsTop coding • Minimax risk • Local differential privacy • Data clearing • Inequality B Hajime Ono

show abstract

Minimax Rates of ℓp-Losses for High-Dimensional Linear Errors-in-Variables Models over ℓq-Balls

Cited by 4 publications

References 26 publications

Overview of High-Dimensional Measurement Error Regression Models

Overview of High-Dimensional Measurement Error Regression Models

Minimax Lower Bounds for High-Dimensional Multi-Response Errors-in-Variables Regression

When should we use top coding in locally private estimation?

Contact Info

Product

Resources

About