{"title":"A new logarithmic multiplicative distortion for correlation analysis","authors":"Siming Deng, Jun Zhang","doi":"10.1002/sam.11708","DOIUrl":null,"url":null,"abstract":"We study the Pearson correlation coefficient in a logarithmic manner under the presence of multiplicative distortion measurement errors. In this context, the observed variables with logarithmic transformation are distorted in multiplicative fashions by an observed confounding variable. The proposed multiplicative distortion model in this paper is applied to analyze positive variables. We utilize the conditional mean calibration and the conditional absolute mean calibration methods to obtain the calibrated variables. Furthermore, we propose confidence intervals based on asymptotic normality, empirical likelihood, and jackknife empirical likelihood. Simulation studies demonstrate the effectiveness of the proposed estimation procedure, and a real‐world example is analyzed to illustrate its practical application.","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Analysis and Data Mining","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1002/sam.11708","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We study the Pearson correlation coefficient in a logarithmic manner under the presence of multiplicative distortion measurement errors. In this context, the observed variables with logarithmic transformation are distorted in multiplicative fashions by an observed confounding variable. The proposed multiplicative distortion model in this paper is applied to analyze positive variables. We utilize the conditional mean calibration and the conditional absolute mean calibration methods to obtain the calibrated variables. Furthermore, we propose confidence intervals based on asymptotic normality, empirical likelihood, and jackknife empirical likelihood. Simulation studies demonstrate the effectiveness of the proposed estimation procedure, and a real‐world example is analyzed to illustrate its practical application.
期刊介绍：
Statistical Analysis and Data Mining addresses the broad area of data analysis, including statistical approaches, machine learning, data mining, and applications. Topics include statistical and computational approaches for analyzing massive and complex datasets, novel statistical and/or machine learning methods and theory, and state-of-the-art applications with high impact. Of special interest are articles that describe innovative analytical techniques, and discuss their application to real problems, in such a way that they are accessible and beneficial to domain experts across science, engineering, and commerce.
The focus of the journal is on papers which satisfy one or more of the following criteria:
Solve data analysis problems associated with massive, complex datasets
Develop innovative statistical approaches, machine learning algorithms, or methods integrating ideas across disciplines, e.g., statistics, computer science, electrical engineering, operation research.
Formulate and solve high-impact real-world problems which challenge existing paradigms via new statistical and/or computational models
Provide survey to prominent research topics.
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