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Preliminary test estimation in system regression models in view of asymmetry

  • J. Kleyn
  • M. Arashi
  • S. Millard
Original Paper
  • 26 Downloads

Abstract

In this paper, we consider the system regression model introduced by Arashi and Roozbeh (Comput Stat 30:359–376, 2015) and study the performance of the feasible preliminary test estimator (FPTE) both analytically and computationally, under the assumption that constraints may hold on the vector parameter space. The performance of the FPTE is analysed through a Monte Carlo simulation study under bounded and or asymmetric loss functions. An application of the so-called Cobb–Douglas production function in economic modelling together with the results from the simulation study shows that the bounded linear exponential (BLINEX) loss function outperforms the linear exponential loss function (LINEX) by comparing risk values.

Keywords

Asymmetric loss BLINEX loss Feasible estimator Preliminary test estimator Seemingly unrelated regression model System regression model 

Notes

Acknowledgements

The authors would like to thank the co-editor and referee for their valuable comments which significantly improved the standard of the paper. This work is based on the research supported in part by the National Research Foundation of South Africa for the Grant TTK1206151317. M. Arashi’s research is supported in part by the National Research Foundation of South Africa (Ref. CPRR160403161466 Grant No. 105840). Any opinion, finding and conclusion or recommendation expressed in this material is that of the author(s) and the NRF does not accept any liability in this regard.

Supplementary material

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Supplementary material 1 (docx 24 KB)
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References

  1. Arashi M (2012) Preliminary test and Stein estimators in simultaneous linear equations. Linear Algebra Appl 436:1195–1211MathSciNetCrossRefMATHGoogle Scholar
  2. Arashi M, Roozbeh M (2015) Shrinkage estimation in system regression model. Comput Stat 30:359–376MathSciNetCrossRefMATHGoogle Scholar
  3. Arashi M, Tabatabaey SMM, Hassanzadeh Bashtian M (2014a) Shrinkage ridge estimators in linear regression. Commun Stat Simul Comput 43:871–904MathSciNetCrossRefMATHGoogle Scholar
  4. Arashi M, Kibria BM, Golam NM, Nadarajah S (2014b) Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model. J Multivar Anal 124:53–74MathSciNetCrossRefMATHGoogle Scholar
  5. Baltagi B (1980) On seemingly unrelated regressions with error components. Econometrica 48:1547–1552MathSciNetCrossRefMATHGoogle Scholar
  6. Brown PJ, Payne C (1975) Election night forecasting (with discussion). J R Stat Soc Ser A 138:463–498CrossRefGoogle Scholar
  7. Casella G, Berger RL (2002) Statistical inference, vol 2. Duxbury Pacific Grove, CAGoogle Scholar
  8. Chib S, Greenberg E (1995) Hierarchical analysis of SUR model with extensions to correlated serial errors and time varying parameter models. J Econom 68:339–360CrossRefMATHGoogle Scholar
  9. Coetsee J, Bekker A, Millard S (2014) Preliminary-test and Bayes estimation of a location parameter under BLINEX loss. Commun Stat Theory Methods 43(17):3641–3660MathSciNetCrossRefMATHGoogle Scholar
  10. Fiebig DG (2001) Seemingly unrelated regression. In: Baltagi B (ed) A companion to theoretical econometrics. Blackwell, Hoboken, pp 101–121Google Scholar
  11. Geweke J (2005) Contemporary Bayesian econometrics and statistics. Wiley, HobokenCrossRefMATHGoogle Scholar
  12. Giles AJ, Giles DA, Ohtani K (1996) The exact risks of some pre-test and Stein-type regression estimators under balanced loss. Commun Stat Theory Methods 25:2901–2924MathSciNetCrossRefMATHGoogle Scholar
  13. Greene WH (2003) Econometric analysis, 5th edn. Prentice-Hall, Upper SaddleGoogle Scholar
  14. Judge GG, Griffiths WE, Hill RC, Lutkepohl H, Lee TC (1985) The theory and practice of econometrics. Wiley, New YorkMATHGoogle Scholar
  15. Kleyn J (2014) The performance of the preliminary test estimator under different loss functions. Ph.D. Dissertation, University of Pretoria, South AfricaGoogle Scholar
  16. Kleyn J, Arashi M, Bekker A, Millard S (2017) Preliminary testing of the Cobb–Douglas production function and related inferential issues. Commun Stat Simul Comput 46:469–488MathSciNetCrossRefMATHGoogle Scholar
  17. Lahiri SN (2003) Resampling methods for dependent data, Springer Series in Statistics. Springer, BerlinCrossRefGoogle Scholar
  18. Meng X, Rubin DB (1996) Efficient methods for estimation and testing with seemingly unrelated regressions in the presence of latent variables and missing observations. In: Berry DA, Chaloner KM, Geweke J (eds) Bayesian analysis in statistics and econometrics: essays in honor of Arnold Zellner. Wiley, New York, pp 215–227Google Scholar
  19. Moon HR (1999) A note on fully-modified estimation ofseemingly unrelated regressions models with integrated regressors. Econ Lett 65:2531CrossRefGoogle Scholar
  20. Moon HR, Perron P (2004) Efficient estimation of SURcointegration regression model and testing for purchasing power parity. Econom Rev 23:293–323CrossRefMATHGoogle Scholar
  21. Muniz G, Kibria BMG (2009) On some ridge regression estimators: an empirical comparisons. Commun Stat Simul Comput 38:621–630MathSciNetCrossRefMATHGoogle Scholar
  22. Percy DF (1996) Zellner’s influence on multivariate linear models. In: Berry DA, Chaloner KM, Geweke J (eds) Bayesian analysis in statistics and econometrics: essays in honor of Arnold Zellner. Wiley, New York, pp 203–213Google Scholar
  23. Quintana JM, Putnam BH, Wilford DS (1998) Mutual and pension funds management: beating the markets using a global Bayesian investment strategy, published in 1996 joint Sect. On Bayesian Statistical Science, American Statistical Association. (www.amstat.org), and International Society for Bayesian Analysis (www.bayesian.org) Proceedings Volume and presented at ISBA Meeting in Istanbul, Turkey, 1995
  24. Raheem SME, Ahmed SE (2011) Positive-shrinkage and pretest estimation in multiple regression: a Monte Carlo study with applications. J Iran Stat Soc 10:267–298MathSciNetMATHGoogle Scholar
  25. Roozbeh M, Arashi M (2013) Feasible ridge estimators in partially linear models. J Multivar Anal 116:35–44MathSciNetCrossRefMATHGoogle Scholar
  26. Roozbeh M, Arashi M, Gasparini M (2012) Seemingly unrelated ridge regression in Semiparametric Models. Commun Stat Theory Methods 41:1364–1386MathSciNetCrossRefMATHGoogle Scholar
  27. Rossi PE, Allenby GM, McCulloch R (2005) Bayesian statistics and marketing. Wiley, HobokenCrossRefMATHGoogle Scholar
  28. Saleh AKME, Kibria BMG (1993) Performance of some new preliminary test ridge regression estimators and their properties. Commun Stat Theory Methods 22:2747–2764MathSciNetCrossRefMATHGoogle Scholar
  29. Srivastava VK, Giles DEA (1987) Seemingly unrelated regression equation models. Marcel Dekker, New YorkMATHGoogle Scholar
  30. Saleh AKME (2006) Theory of preliminary test and Stein-type estimation with applications. Wiley, New YorkCrossRefMATHGoogle Scholar
  31. Srivastava VK, Maekawa K (1995) Efficiency properties of feasible generalized least squares estimators in SURE models under non-normal disturbances. J Econom 66:99–121MathSciNetCrossRefMATHGoogle Scholar
  32. Tabatabaey SMM, Saleh AKME, Kibria BMG (2004) Simultaneous estimation of regression parameters with spherically symmetric errors under possible stochastic constraints. Int J Stat Sci 3:1–20Google Scholar
  33. Theil H (1971) Principles of econometrics. Wiley, New YorkMATHGoogle Scholar
  34. Wen D, Levy S (2001) BLINEX: a bounded asymmetric loss function with application to Bayesian estimation. Commun Stat Theory Methods 30(1):147–153MathSciNetCrossRefMATHGoogle Scholar
  35. Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J Am Stat Assoc 57:348–368MathSciNetCrossRefMATHGoogle Scholar
  36. Zellner A (1963) Estimators for seemingly unrelated regressions: some exact finite sample results. J Am Stat Assoc 58:977–992; corrigendum, (1972), 67, 255Google Scholar
  37. Zellner A, Huang DS (1962) Further properties of efficient estimators for seemingly unrelated regression equations. Int Econ Rev 3:300–313CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Natural and Agricultural SciencesUniversity of PretoriaPretoriaSouth Africa
  2. 2.University of PretoriaPretoriaSouth Africa
  3. 3.Shahrood University of TechnologyShahroodIran

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