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Kernel Estimation When Density May Not Exist: A Corrigendum

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  • Zinde-Walsh, Victoria

Abstract

The paper “Kernel estimation when density may not exist” (Zinde-Walsh, 2008) considered density as a generalized function given by a functional on a space of smooth functions; this made it possible to establish the limit properties of the kernel estimator without assuming the existence of the density function. This note corrects an error in that paper in the derivation of the variance of the kernel estimator. The corrected result is that in the space of generalized functions the parametric rate of convergence of the kernel density estimator to the limit Gaussian process is achievable.

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  • Zinde-Walsh, Victoria, 2017. "Kernel Estimation When Density May Not Exist: A Corrigendum," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1259-1263, October.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:05:p:1259-1263_00
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    References listed on IDEAS

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    1. Victoria Zinde-Walsh & Peter C.B. Phillips, 2003. "Fractional Brownian Motion as a Differentiable Generalized Gaussian Process," Cowles Foundation Discussion Papers 1391, Cowles Foundation for Research in Economics, Yale University.
    2. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1172-1196, October.
    3. Green, David A & Riddell, W Craig, 1997. "Qualifying for Unemployment Insurance: An Empirical Analysis," Economic Journal, Royal Economic Society, vol. 107(440), pages 67-84, January.
    4. Frigyesi, Attila & Hössjer, Ola, 1998. "A test for singularity," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 215-226, October.
    5. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(5), pages 912-951, October.
    6. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    7. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    8. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    9. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
    10. Lu, Zhan-Qian, 1999. "Nonparametric Regression with Singular Design," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 177-201, August.
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    1. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2021. "Rates of Expansions for Functional Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 121-139, December.
    2. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2022. "Correction to: Rates of Expansions for Functional Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(2), pages 487-487, June.
    3. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Monash Econometrics and Business Statistics Working Papers 18/21, Monash University, Department of Econometrics and Business Statistics.
    4. Byung-hill Jun & Hosin Song, 2019. "Tests for Detecting Probability Mass Points," Korean Economic Review, Korean Economic Association, vol. 35, pages 205-248.
    5. Meho Saša Kovačević & Lovorka Librić & Gordana Ivoš & Anita Cerić, 2020. "Application of Reliability Analysis for Risk Ranking in a Levee Reconstruction Project," Sustainability, MDPI, vol. 12(4), pages 1-17, February.
    6. ZINDE-WALSH, Victoria, 2007. "Errors-in-Variables Models : A Generalized Functions Approach," Cahiers de recherche 14-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.

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