Open Access
October 2018 Goodness-of-fit testing of error distribution in linear measurement error models
Hira L. Koul, Weixing Song, Xiaoqing Zhu
Ann. Statist. 46(5): 2479-2510 (October 2018). DOI: 10.1214/17-AOS1627


This paper investigates a class of goodness-of-fit tests for fitting an error density in linear regression models with measurement error in covariates. Each test statistic is the integrated square difference between the deconvolution kernel density estimator of the regression model error density and a smoothed version of the null error density, an analog of the so-called Bickel and Rosenblatt test statistic. The asymptotic null distributions of the proposed test statistics are derived for both the ordinary smooth and super smooth cases. The asymptotic power behavior of the proposed tests against a fixed alternative and a class of local nonparametric alternatives for both cases is also described. The finite sample performance of the proposed test is evaluated by a simulation study. The simulation study shows some superiority of the proposed test over some other tests. Finally, a real data is used to illustrate the proposed test.


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Hira L. Koul. Weixing Song. Xiaoqing Zhu. "Goodness-of-fit testing of error distribution in linear measurement error models." Ann. Statist. 46 (5) 2479 - 2510, October 2018.


Received: 1 September 2015; Revised: 1 July 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964339
MathSciNet: MR3845024
Digital Object Identifier: 10.1214/17-AOS1627

Primary: 62G10
Secondary: 62G20

Keywords: $L_{2}$-distance tests , Deconvolution density estimators

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 5 • October 2018
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