Specification testing for errors-in-variables models
This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the method proposed by Hall and Ma (2007), our test allows general nonlinear regression models. Since our test employs the smoothing approach, it complements the nonsmoothing one by Hall and Main terms of local power properties. The other existing method, by Song (2008), is shown to possess trivial power under certain alternatives. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities and develop a bootstrap method to approximate the critical value. We apply the test to the specification of Engel curves in the US. Finally, some simulation results endorse our theoretical findings: our test has advantages in detecting high frequency alternatives and dominates the existing tests under certain specifications.
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References listed on IDEAS
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- Hajo Holzmann & Leif Boysen, 2006. "Integrated Square Error Asymptotics for Supersmooth Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 849-860.
- Song, Weixing, 2008. "Model checking in errors-in-variables regression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2406-2443, November.
- Miguel A. Delgado & Manuel A. Dominguez & Pascal Lavergne, 2006. "Consistent Tests of Conditional Moment Restrictions," Annals of Economics and Statistics, GENES, issue 81, pages 33-67.
- Wangli Xu & Lixing Zhu, 2015. "Nonparametric check for partial linear errors-in-covariables models with validation data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 793-815, August.
- Song, Weixing, 2009. "Lack-of-fit testing in errors-in-variables regression model with validation data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 765-773, March.
- repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
- Bert Van Es & Hae-Won Uh, 2005. "Asymptotic Normality of Kernel-Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483.
- Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
- Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995.
"Nonlinear errors in variables Estimation of some Engel curves,"
Journal of Econometrics,
Elsevier, vol. 65(1), pages 205-233, January.
- J. A. Hausman & W. K. Newey & J. L. Powel, 1988. "Nonlinear Errors in Variables: Estimation of Some Engel Curves," Working papers 504, Massachusetts Institute of Technology (MIT), Department of Economics.
- Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
- repec:adr:anecst:y:2006:i:81 is not listed on IDEAS
- Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
- Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
- Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.
- Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
- Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January. Full references (including those not matched with items on IDEAS)
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