{"title":"Nonparametric regression with responses missing at random and the scale depending on auxiliary covariates","authors":"Tian Jiang","doi":"10.1080/10485252.2022.2149749","DOIUrl":null,"url":null,"abstract":"Nonparametric regression with missing at random (MAR) responses, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that both heteroscedasticity and MAR mechanism affect the sharp constant of the minimax mean integrated squared error (MISE) convergence. Our sharp minimax procedure is based on the estimation of unknown nuisance scale function, design density and availability likelihood. The estimator is adaptive to the missing mechanism and unknown smoothness of the estimated regression function. Simulation studies and real examples also justify practical feasibility of the proposed method for this complex regression setting.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"4 1","pages":"302 - 322"},"PeriodicalIF":0.8000,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonparametric Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10485252.2022.2149749","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Nonparametric regression with missing at random (MAR) responses, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that both heteroscedasticity and MAR mechanism affect the sharp constant of the minimax mean integrated squared error (MISE) convergence. Our sharp minimax procedure is based on the estimation of unknown nuisance scale function, design density and availability likelihood. The estimator is adaptive to the missing mechanism and unknown smoothness of the estimated regression function. Simulation studies and real examples also justify practical feasibility of the proposed method for this complex regression setting.
期刊介绍：
Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics:
Nonparametric modeling,
Nonparametric function estimation,
Rank and other robust and distribution-free procedures,
Resampling methods,
Lack-of-fit testing,
Multivariate analysis,
Inference with high-dimensional data,
Dimension reduction and variable selection,
Methods for errors in variables, missing, censored, and other incomplete data structures,
Inference of stochastic processes,
Sample surveys,
Time series analysis,
Longitudinal and functional data analysis,
Nonparametric Bayes methods and decision procedures,
Semiparametric models and procedures,
Statistical methods for imaging and tomography,
Statistical inverse problems,
Financial statistics and econometrics,
Bioinformatics and comparative genomics,
Statistical algorithms and machine learning.
Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order.
Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.
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