Article
Mathematics
Saulius Jokubaitis, Remigijus Leipus
Summary: This paper studies the asymptotic normality in high-dimensional linear regression, focusing on the case where the covariance matrix of the regression variables has a KMS structure. The main result is the derivation of the exact asymptotic distribution for the squared norm of the product between predictor matrix X and outcome variable Y, under rather unrestrictive assumptions for the model parameters. A Monte Carlo simulation study is conducted for a specific case of approximate sparsity of the model parameter vector beta.
Article
Statistics & Probability
Pratik Ramprasad, Yuantong Li, Zhuoran Yang, Zhaoran Wang, Will Wei Sun, Guang Cheng
Summary: The recent emergence of reinforcement learning has led to a demand for robust statistical inference methods. Existing methods for inference in online learning are not applicable in RL, this article explores the use of the online bootstrap method in RL policy evaluation and demonstrates its effectiveness through experiments.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2022)
Article
Automation & Control Systems
Louna Alsouki, Laurent Duval, Clement Marteau, Rami El Haddad, Francois Wahl
Summary: Relating variables X to response y is important in chemometrics. Qualitative interpretation can enhance quantitative prediction by identifying influential features. Projections (e.g. PLS) and variable selections (e.g. lasso) are used for dimension reduction in high-dimensional problems. Dual-sPLS, a variant of PLS1, provides a balance between accurate prediction and efficient interpretation through penalizations inspired by classical regression methods and the dual norm notion. It performs favorably compared to similar regression methods on simulated and real chemical data.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2023)
Article
Geosciences, Multidisciplinary
R. M. Di Biase, A. Marcelli, S. Franceschi, A. Bartolini, L. Fattorini
Summary: The difference between potential and actual distribution of species is emphasized, highlighting the ecological importance of maps depicting the actual presence of species in the study region. Estimation of species presence at any location within the study region is achieved by recording presence/absence within plots centered at sample locations. Nearest-neighbour interpolator is used in a design-based framework for estimation.
SPATIAL STATISTICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yanjin Peng, Lei Wang
Summary: In this paper, the authors propose a two-stage online debiased lasso estimation and statistical inference method for high-dimensional quantile regression models in the presence of streaming data. The method modifies the quantile regression score function and carries out an online debiasing procedure to effectively estimate the quantile regression models in streaming data and establish the asymptotic normality of the resulting estimator.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2023)
Article
Mathematical & Computational Biology
R. A. P. H. A. E. L. A. FRASER, S. T. U. A. R. T. R. LIPSITZ, D. E. B. A. J. Y. O. T. I. SINHA, G. A. R. R. E. T. T. M. FITZMAURICE
Summary: There is a need for statistical methods to analyze skewed responses in complex sample surveys. This study proposes using quantile regression to address this problem, and shows how to correctly estimate the variance by considering the survey design. The results demonstrate that the variance of the median regression estimator has minimal bias and appropriate coverage probability. The motivation for this work comes from the National Health and Nutrition Examination Survey, where the impact of the results on iodine deficiency in females compared to males with adjustment for other covariates is demonstrated.
Article
Computer Science, Information Systems
Jana Jankova, Sara van de Geer
Summary: Sparse principal component analysis has become widely used for dimensionality reduction, and this paper proposes a methodology for uncertainty quantification with construction of confidence intervals and tests for the principal eigenvector. The novel estimator achieves minimax optimal rates, has a Gaussian limiting distribution, and can be used for hypothesis testing and support recovery of the first eigenvector. The empirical performance of the new estimator is demonstrated on synthetic data and shown to compare favorably with classical PCA in moderately high-dimensional regimes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Statistics & Probability
Zhaohan Hou, Wei Ma, Lei Wang
Summary: This paper investigates statistical learning in the presence of heavy-tailed and/or asymmetric errors by considering the inherent distribution of the data. The composite quantile regression (CQR) estimator is proposed as a robust and efficient alternative to the ordinary least squares and single quantile regression estimators. Two classes of sparse and debiased lasso CQR estimation and inference methods are proposed based on aggregated and communication-efficient approaches. The performance of the proposed estimators is evaluated through simulations and a real-world dataset.
Article
Economics
Jun Ma, Vadim Marmer, Artyom Shneyerov, Pai Xu
Summary: This study introduces a new nonparametric estimator for estimating the probability density of latent valuations in first-price auctions, which imposes the monotonicity constraint on the estimated inverse bidding strategy. The estimator shows a smaller asymptotic variance compared to previous methods, and a bootstrap-based approach is provided to construct uniform confidence bands for the density function.
ECONOMETRIC REVIEWS
(2021)
Article
Statistics & Probability
George Karabatsos
Summary: Approximate Bayesian computation (ABC) is a method that allows inference of the posterior distribution for models with intractable likelihoods by using a tractable approximate likelihood. This study proposes and investigates new ABC methods based on asymptotically normal and consistent point-estimators, and validates them through simulations and real data analysis.
COMPUTATIONAL STATISTICS
(2023)
Article
Statistics & Probability
Kara-Terki Nesrine
Summary: This article obtains the conditions of local asymptotic normality (LAN) and uniform local asymptotic normality (ULAN) for a linear functional autoregressive process using a martingale central limit theorem. As a consequence, asymptotically efficient tests for determining the order are constructed. An example is discussed as a special case.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Mathematics
Martin Hrba, Matus Maciak, Barbora Pestova, Michal Pesta
Summary: Classical normal asymptotics can pose challenges in statistical inference due to unknown and difficult-to-estimate parameters in the limit distributions. Bootstrap methods offer a plausible alternative and a methodological framework for non-independent and non-identically distributed data is presented, along with theoretical justification. These methods have been applied in insurance and psychometry.
Article
Mathematics, Applied
Siddhartha Chakraborty, Biswabrata Pradhan
Summary: This study proposes two estimators of cumulative residual extropy and compares their performance with an existing kernel based estimator through simulation. The asymptotic properties of the estimators are examined, and two estimators of quantile cumulative residual extropy measure are also proposed, demonstrating their consistency and asymptotic normality. The proposed estimators show good performance through analysis of two data sets.
RICERCHE DI MATEMATICA
(2023)
Article
Physics, Multidisciplinary
Eugene A. Opoku, Syed Ejaz Ahmed, Farouk S. Nathoo
Summary: The study proposes an efficient estimation strategy for high-dimensional data applications and explores methods for estimating fixed effects parameters in LMM when prior information is available. By comparing the performance of different estimation strategies, it investigates their performance in simulation studies and in the context of investigating the relationship between brain connectivity and genetics in Alzheimer's disease.
Article
Statistics & Probability
Ozge Kuran, Secil Yalaz
Summary: This article proposes a new kernel prediction method using ridge regression to address the issue of multicollinearity and its impact on various aspects of the partially linear mixed measurement error model. The article provides theoretical analysis and empirical evaluation to assess the feasibility of the method.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2022)
Article
Multidisciplinary Sciences
Adam Bloniarz, Hanzhong Liu, Cun-Hui Zhang, Jasjeet S. Sekhon, Bin Yu
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2016)
Article
Biology
Hanzhong Liu, Yuehan Yang
Article
Statistics & Probability
Hanzhong Liu, Xin Xu, Jingyi Jessica Li