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Semiparametric Estimation of Regression Functions Under Shape Invariance Restrictions

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  • Wilke, Ralf A.

Abstract

This paper considers the shape invariant modelling approach in semiparametric regression estimation. Nonparametric functions of similar shape are linked by parametric transformations with unknown parameters. A computationally convenient estimation procedure is suggested. √N- consistency of the parameter estimates is proved. Finite sample performance of this estimator is investigated by simulations. An application to consumer data illustrates the importance of this method for applied statistics. Estimations indicate that the imposed shape invariance restrictions have empirical evidence in the semiparametric modelling of consumer demand.

Suggested Citation

  • Wilke, Ralf A., 2003. "Semiparametric Estimation of Regression Functions Under Shape Invariance Restrictions," ZEW Discussion Papers 03-64, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:1494
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    File URL: https://www.econstor.eu/bitstream/10419/23998/1/dp0364.pdf
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    References listed on IDEAS

    as
    1. Ralf A. Wilke, 2006. "Semi-parametric estimation of consumption-based equivalence scales: the case of Germany," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 781-802.
    2. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    3. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    5. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
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    Cited by:

    1. Ralf A. Wilke, 2006. "Semi-parametric estimation of consumption-based equivalence scales: the case of Germany," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 781-802.
    2. repec:ebl:ecbull:v:4:y:2007:i:21:p:1-11 is not listed on IDEAS
    3. Thanasis Stengos & Dianqin Wang, 2007. "Testing for Shape Invariance of Semiparametric Equivalence Scales," Economics Bulletin, AccessEcon, vol. 4(21), pages 1-11.

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    More about this item

    Keywords

    shape invariant modelling; semiparametric regression; simulations; large sample properties; consumer data;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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