A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem

被引:72
作者
Delaigle, Aurore [1 ,2 ]
Fan, Jianqing [3 ,4 ]
Carroll, Raymond J. [5 ]
机构
[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia
[3] Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ 08544 USA
[4] Shanghai Univ Finance & Econ, Dept Stat, Shanghai, Peoples R China
[5] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
基金
澳大利亚研究理事会; 美国国家科学基金会;
关键词
Bandwidth selector; Deconvolution; Inverse problems; Local polynomial; Measurement errors; Nonparametric regression; Replicated measurements; NONPARAMETRIC REGRESSION; SIMULATION-EXTRAPOLATION; DENSITY-ESTIMATION; DECONVOLUTION PROBLEM; ASYMPTOTIC NORMALITY; OPTIMAL RATES; MODELS; CONVERGENCE; CHOICE;
D O I
10.1198/jasa.2009.0114
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
Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however. is not straightforward and has remained an open problem for the last 15 years. We propose an innovative local polynomial estimator of any order in the errors-in-variables context, derive its design-adaptive asymptotic properties and study its finite sample performance on simulated examples. We provide not only a solution to a long-standing open problem, but also provide methodological contributions to error-invariable regression, including local polynomial estimation of derivative functions.
引用
收藏
页码:348 / 359
页数:12
相关论文
共 42 条
[1]   Bayesian smoothing and regression splines for measurement error problems [J].
Berry, SM ;
Carroll, RJ ;
Ruppert, D .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2002, 97 (457) :160-169
[2]   Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model [J].
Butucea, C ;
Matias, C .
BERNOULLI, 2005, 11 (02) :309-340
[3]  
Carroll R. J., 2006, MEASUREMENT ERROR NO, DOI DOI 10.1201/9781420010138
[4]   Nonparametric regression in the presence of measurement error [J].
Carroll, RJ ;
Maca, JD ;
Ruppert, D .
BIOMETRIKA, 1999, 86 (03) :541-554
[5]   Low order approximations in deconvolution and regression with errors in variables [J].
Carroll, RJ ;
Hall, P .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2004, 66 :31-46
[6]   OPTIMAL RATES OF CONVERGENCE FOR DECONVOLVING A DENSITY [J].
CARROLL, RJ ;
HALL, P .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1988, 83 (404) :1184-1186
[7]  
Comte F, 2007, STAT SINICA, V17, P1065
[8]   SIMULATION-EXTRAPOLATION ESTIMATION IN PARAMETRIC MEASUREMENT ERROR MODELS [J].
COOK, JR ;
STEFANSKI, LA .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1994, 89 (428) :1314-1328
[9]  
DELAIGLE A, 2008, DESIGN ADAPTIVE LOCA
[10]  
Delaigle A, 2008, STAT SINICA, V18, P1025