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Semiparametric Deconvolution with Unknown Error Variance

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Abstract

Deconvolution is a useful statistical technique for recovering an unknown density in the presence of measurement error. Typically, the method hinges on stringent assumptions about teh nature of the measurement error, more specifically, that the distribution is *entirely* known. We relax this assumption in the context of a regression error component model and develop an estimator for the unkinown density. We show semi-uniform consistency of the estimator and provide Monte Carlo evidence that demonstrates the merits of the method.

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  • William C. Horrace & Christopher F. Parmeter, 2008. "Semiparametric Deconvolution with Unknown Error Variance," Center for Policy Research Working Papers 104, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:104
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    Cited by:

    1. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2020. "Robust frontier estimation from noisy data: A Tikhonov regularization approach," Econometrics and Statistics, Elsevier, vol. 14(C), pages 1-23.
    2. William C. Horrace & Ian A. Wright, 2020. "Stationary Points for Parametric Stochastic Frontier Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 516-526, July.
    3. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    4. Dai, Xiaofeng, 2016. "Non-parametric efficiency estimation using Richardson–Lucy blind deconvolution," European Journal of Operational Research, Elsevier, vol. 248(2), pages 731-739.
    5. William C. Horrace & Christopher F. Parmeter, 2018. "A Laplace stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 37(3), pages 260-280, March.
    6. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2021. "Density deconvolution with Laplace errors and unknown variance," Journal of Productivity Analysis, Springer, vol. 56(2), pages 103-113, December.
    7. Zhou, Jianhua & Parmeter, Christopher F. & Kumbhakar, Subal C., 2020. "Nonparametric estimation of the determinants of inefficiency in the presence of firm heterogeneity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1142-1152.
    8. William C. Horrace & Yulong Wang, 2022. "Nonparametric tests of tail behavior in stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 537-562, April.
    9. Alessandro Bonanno & Francesco Bimbo & Marco Costanigro & Alfons Oude Lansink & Rosaria Viscecchia, 2019. "Credence attributes and the quest for a higher price – a hedonic stochastic frontier approach," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 46(2), pages 163-192.
    10. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    12. Qu Feng & William Horrace & Guiying Laura Wu, 2013. "Wrong Skewness and Finite Sample Correction in Parametric Stochastic Frontier Models Abstract: In parametric stochastic frontier models, the composed error is specified as the sum of a two-sided noise," Center for Policy Research Working Papers 154, Center for Policy Research, Maxwell School, Syracuse University.
    13. Fan Zhang & Joshua Hall & Feng Yao, 2018. "Does Economic Freedom Affect The Production Frontier? A Semiparametric Approach With Panel Data," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1380-1395, April.
    14. Phill Wheat & Alexander D. Stead & William H. Greene, 2019. "Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England," Journal of Productivity Analysis, Springer, vol. 51(1), pages 21-38, February.
    15. Anaya, Karim L. & Pollitt, Michael G., 2017. "Using stochastic frontier analysis to measure the impact of weather on the efficiency of electricity distribution businesses in developing economies," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1078-1094.
    16. Taining Wang & Feng Yao & Subal C. Kumbhakar, 2024. "A flexible stochastic production frontier model with panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(4), pages 564-588, June.
    17. Jun Cai & William C. Horrace & Christopher F. Parmeter, 2024. "Penalized sieve estimation of zero‐inefficiency stochastic frontiers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 41-65, January.
    18. Yiping Yang & Tiejun Tong & Gaorong Li, 2019. "SIMEX estimation for single-index model with covariate measurement error," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 137-161, March.

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    More about this item

    Keywords

    Error component; ordinary smooth; semi-uniform consistency;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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