Nonparametric regression with responses missing at random and the scale depending on auxiliary covariates

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2022-11-25 DOI:10.1080/10485252.2022.2149749

Tian Jiang

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.

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随机缺失响应的非参数回归和依赖于辅助协变量的尺度

考虑了随机缺失(MAR)响应的非参数回归，感兴趣的单变量回归成分以及依赖于预测变量和辅助协变量的尺度函数。渐近理论表明，异方差和MAR机制都影响最小最大平均积分平方误差(MISE)收敛的锐常数。我们的锐极小极大程序是基于对未知妨害尺度函数、设计密度和可用性可能性的估计。该估计器能够适应估计回归函数的缺失机制和未知平滑性。仿真研究和实际算例也证明了该方法对这种复杂回归设置的实际可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

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.