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Estimating multivariate density and its derivatives for mixed measurement error data
被引:1
作者:
Guo, Linruo
[1
]
Song, Weixing
[1
]
Shi, Jianhong
[2
]
机构:
[1] Kansas State Univ, Dept Stat, Manhattan, KS 66506 USA
[2] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041000, Peoples R China
基金:
中国国家自然科学基金;
关键词:
Asymptotic normality;
Classical and deconvolution kernel;
Convergence rate;
Measurement error;
Ordinary and super smooth;
ASYMPTOTIC NORMALITY;
REGRESSION ESTIMATION;
OPTIMAL RATES;
DECONVOLUTION;
CONVERGENCE;
BERKSON;
MIXTURE;
D O I:
10.1016/j.jmva.2022.105005
中图分类号:
O21 [概率论与数理统计];
C8 [统计学];
学科分类号:
020208 ;
070103 ;
0714 ;
摘要:
In this paper, we propose a nonparametric mixed kernel estimator for a multivariate density function and its derivatives when the data are contaminated with different sources of measurement errors. The proposed estimator is a mixture of the classical and the deconvolution kernels, accounting for the error-free and error-prone variables, respectively. Large sample properties of the proposed nonparametric estimator, includ-ing the order of the mean squares error, the consistency, and the asymptotic normality, are thoroughly investigated. The optimal convergence rates among all nonparametric estimators for different measurement error structures are derived, and it is shown that the proposed mixed kernel estimators achieve the optimal convergence rate. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. (C) 2022 Elsevier Inc. All rights reserved.
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页数:18
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