{"title":"Uniform convergence rates and automatic variable selection in nonparametric regression with functional and categorical covariates","authors":"Leonie Selk","doi":"10.1080/10485252.2023.2207673","DOIUrl":null,"url":null,"abstract":"In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are developed. A uniform rate of convergence for the regression / classification estimator is given. Further it is shown that, asymptotically, a data-driven least squares cross-validation method can automatically remove irrelevant, noise variables.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2022-09-29","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/10.1080/10485252.2023.2207673","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
In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are developed. A uniform rate of convergence for the regression / classification estimator is given. Further it is shown that, asymptotically, a data-driven least squares cross-validation method can automatically remove irrelevant, noise variables.
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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