Skip to main content
SpringerLink
Log in

Expectile and M-quantile regression for panel data

  • Original Paper
  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

Linear fixed effect models are a general way to fit panel or longitudinal data with a distinct intercept for each unit. Based on expectile and M-quantile approaches, we propose alternative regression estimation methods to estimate the parameters of linear fixed effect models. The estimation functions are penalized by the least absolute shrinkage and selection operator to reduce the dimensionality of the data. Some asymptotic properties of the estimators are established, and finite sample size investigations are conducted to verify the empirical performances of the estimation methods. The computational implementations of the procedures are discussed, and real economic panel data from the Organisation for Economic Cooperation and Development are analyzed to show the usefulness of the methods in a practical problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Algorithm 1
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. Collected on May 26, 2022.

References

  • Alemu, A.M.: The effect of R &D on high-tech product export competitiveness: empirical evidence from panel data of east Asian economies. STI Policy Rev. 3(1), 46–62 (2012)

    Google Scholar 

  • Alfò, M., Marino, M.F., Ranalli, M.G., Salvati, N., Tzavidis, N.: M-quantile regression for multivariate longitudinal data with an application to the Millennium Cohort study. J. R. Stat. Soc. C 70(1), 122–146 (2021)

    Article  MathSciNet  Google Scholar 

  • Baesu, V., Albulescu, C.T., Farkas, Z.-B., Draghici, A.: (2015). Determinants of the high-tech sector innovation performance in the European union: a review. In: Proc. Technol., 19:371–378. 8th International Conference Interdisciplinarity in Engineering, INTER-ENG: 9–10 October 2014. Tirgu Mures, Romania (2014)

  • Barry, A., Oualkacha, K., Charpentier, A.: Alternative fixed-effects panel model using weighted asymmetric least squares regression. Stat. Methods Appl. 32(3), 819–841 (2023)

    Article  MathSciNet  Google Scholar 

  • Breckling, J., Chambers, R.: M-quantiles. Biometrika 75(4), 761–771 (1988)

    Article  MathSciNet  Google Scholar 

  • Breckling, J., Kokic, P., Lubke, O.: A note on multivariate M-quantiles. Stat. Probab. Lett. 55, 39–44 (2001)

    Article  MathSciNet  Google Scholar 

  • Danilevicz, I.M., Reisen, V.A., Bondon, P.: pqrfe: penalized quantile regression with fixed effects. R Package Version 1, 1 (2022)

    Google Scholar 

  • Diggle, P.: An approach to the analysis of repeated measurements. Biometrics 44(4), 959–971 (1988)

    Article  MathSciNet  PubMed  Google Scholar 

  • Eddelbuettel, D., Sanderson, C.: RcppArmadillo: accelerating R with high-performance C++ linear algebra. Comput. Stat. Data Anal. 71, 1054–1063 (2014)

    Article  MathSciNet  Google Scholar 

  • Falk, M.: High-tech exports and economic growth in industrialized countries. Appl. Econ. Lett. 16(10), 1025–1028 (2009)

    Article  Google Scholar 

  • Galarza, C., Castro, L., Louzada, F., Lachos, V.: Quantile regression for nonlinear mixed effects models: a likelihood based perspective. Stat. Pap. 61, 1281–1307 (2020)

    Article  MathSciNet  Google Scholar 

  • Galvão, A.F., Gu, J., Volgushev, S.: On the unbiased asymptotic normality of quantile regression with fixed effects. J. Econ. 218(1), 178–215 (2020)

    Article  MathSciNet  Google Scholar 

  • Geraci, M., Bottai, M.: Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics 8(1), 140–154 (2007)

    Article  PubMed  Google Scholar 

  • Geraci, M., Bottai, M.: Linear quantile mixed models. Stat. Comput. 24, 461–479 (2014)

    Article  MathSciNet  Google Scholar 

  • Horowitz, J.L., Lee, S.S.: Semiparametric estimation of a panel data proportional hazards model with fixed effects. J. Econ. 119(1), 155–198 (2004)

    Article  MathSciNet  Google Scholar 

  • Huber, P.J.: Robust Estimation of a Location Parameter. Ann. Stat. 1(53), 73–101 (1964)

    Article  MathSciNet  Google Scholar 

  • Jones, M.C.: Expectiles and M-quantiles are quantiles. Stat. Probab. Lett. 20(2), 149–153 (1994)

    Article  MathSciNet  Google Scholar 

  • Kim, J., Oh, H.-S.: Pseudo-quantile functional data clustering. J. Multivar. Anal. 178, 104626 (2020)

    Article  MathSciNet  Google Scholar 

  • Knight, K., Fu, W.: Asymptotics for Lasso-type estimators. Ann. Stat. 28, 1356–1378 (2000)

    MathSciNet  Google Scholar 

  • Koenker, R.: Quantile regression for longitudinal data. J. Multivar. Anal. 91(1), 74–89 (2004)

    Article  MathSciNet  Google Scholar 

  • Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  • Koenker, R., Bassett, G., Jr.: Regression quantiles. Econometrica 46, 33–50 (1978)

    Article  MathSciNet  Google Scholar 

  • Kokic, P., Breckling, J., Lübke, O.: A new definition of multivariate M-quantiles. In: Dodge, Y. (ed.) Statistical Data Analysis Based on the L1-Norm and Related Methods, pp. 15–24. Birkhäuser Basel, Basel (2002)

    Chapter  Google Scholar 

  • Laird, N.M., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38(4), 963–974 (1982)

    Article  PubMed  Google Scholar 

  • Lamarche, C.: Robust penalized quantile regression estimation for panel data. J. Econ. 157(2), 396–408 (2010)

    Article  MathSciNet  Google Scholar 

  • Lamarche, C., Parker, T.: (2021). Wild bootstrap inference for penalized quantile regression for longitudinal data. Working paper or preprint

  • Li, D., Wang, L., Zhao, W.: Estimation and inference for Multikink expectile regression with longitudinal data. Stat. Med. 41(7), 1296–1313 (2022)

    Article  MathSciNet  PubMed  Google Scholar 

  • Li, H., Liu, Y., Luo, Y.: Double penalized quantile regression for the linear mixed effects model. J. Syst. Sci. Complex. 33, 2080–2102 (2020)

    Article  MathSciNet  Google Scholar 

  • Marino, M., Farcomeni, A.: Linear quantile regression models for longitudinal experiments: an overview. Metron 73, 229–247 (2015)

    Article  MathSciNet  Google Scholar 

  • Newey, W., Powell, J.: Asymmetric least squares estimation and testing. Econometrica 55(4), 819–847 (1987)

    Article  MathSciNet  Google Scholar 

  • Schnabel, S., Eilers, P.: Optimal expectile smoothing. Comput. Stat. Data Anal. 53, 4168–4177 (2009)

    Article  MathSciNet  Google Scholar 

  • Tian, Y., Wang, L., Tang, M., Tian, M.: Weighted composite quantile regression for longitudinal mixed effects models with application to AIDS studies. Commun. Stat. Simul. Comput. 50(6), 1837–1853 (2021)

    Article  MathSciNet  Google Scholar 

  • Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58(1), 267–288 (1996)

    MathSciNet  Google Scholar 

  • Turen, U., Gökmen, Y.: The determinants of high technology exports volume: a panel data analysis of eu-15 countries. Int. J. Econ. Manag. Soc. Sci. 2(3), 217–232 (2013)

    Google Scholar 

  • Tzavidis, N., Salvati, N., Schmid, T., Flouri, E., Midouhas, E.: Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort study children in England using M-quantile random-effects regression. J. R. Stat. Soc. A 179(2), 427–452 (2016)

    Article  MathSciNet  Google Scholar 

  • Waltrup, L.S., Kauermann, G.: Smooth expectiles for panel data using penalized splines. Stat. Comput. 27, 271–282 (2017)

  • Waltrup, L.S., Sobotka, F., Kneib, T., Kauermann, G.: Expectile and quantile regression - David and Goliath? Stat. Model. 15(5), 433–456 (2015)

    Article  MathSciNet  Google Scholar 

  • Wang, H.J., Li, D., He, X.: Estimation of high conditional quantiles for heavy-tailed distributions. J. Am. Stat. Assoc. 107(500), 1453–1464 (2012)

    Article  MathSciNet  Google Scholar 

  • Yoo, S.-H.: High-technology exports and economic output: an empirical investigation. Appl. Econ. Lett. 15(7), 523–525 (2008)

    Article  ADS  Google Scholar 

  • You, J., Zhou, X.: Asymptotic theory in fixed effects panel data seemingly unrelated partially linear regression models. Econ. Theory 30(2), 407–435 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank two anonymous reviewers for their valuable comments to improve the quality of the paper.

Funding

Part of this paper was written when Valdério Anselmo Reisen was visiting CentraleSupélec. This author is indebted to CentraleSupélec, CNPq and FAPES for their financial support. Ian Meneghel Danilevicz is indebted to Université Paris-Saclay and CAPES for their financial support. This research was also supported by DATAIA Convergence Institute as part of the Programme d’Investissement d’Avenir (ANR17-CONV-0003) operated by Université Paris-Saclay.

Author information

Authors and Affiliations

  1. Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Ian Meneghel Danilevicz & Valdério Anselmo Reisen

  2. CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Université Paris-Saclay, 91190, Gif-sur-Yvette, France

    Ian Meneghel Danilevicz, Valdério Anselmo Reisen & Pascal Bondon

  3. Graduate Program in Environmental Engineer, Graduate Program in Economics, Universidade Federal do Espírito Santo, Vitória, Brazil

    Valdério Anselmo Reisen

  4. Institute of Mathematics and Statistics, Universidade Federal da Bahia, Salvador, Brazil

    Valdério Anselmo Reisen

Authors
  1. Ian Meneghel Danilevicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valdério Anselmo Reisen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pascal Bondon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ian Meneghel Danilevicz.

Ethics declarations

Conflicts of interest

The authors declare no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danilevicz, I.M., Reisen, V.A. & Bondon, P. Expectile and M-quantile regression for panel data. Stat Comput 34, 97 (2024). https://doi.org/10.1007/s11222-024-10396-7

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s11222-024-10396-7

Keywords

Search

Navigation