Research Article
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Evaluation of Two Stage Modified Ridge Estimator and Its Performance

Year 2018, Volume: 22 Issue: 6, 1631 - 1637, 01.12.2018
https://doi.org/10.16984/saufenbilder.377423

Abstract

Biased
estimation methods are more desirable than two stage least squares estimation
for simultaneous equations models suffering from the problem of
multicollinearity. This problem is also handled by using some prior information.
Taking account of this knowledge, we recommend two stage modified ridge
estimator. The new estimator can also be evaluated as an alternative to the
previously proposed two stage ridge estimator. The widespread performance
criterion, mean square error, is  taken
into consideration to compare the two stage modified ridge, two stage ridge and
two stage least squares estimators. A real life data analysis is investigated
to prove the theoretical results in practice. In addition, t
he
intervals of the biasing parameter which provide the superiority of the two
stage modified ridge estimator are determined 
 with the help of figures. The
researchers who deal with simultaneous systems with multicollinearity can opt for
the two stage modified ridge estimator.

References

  • A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, vol. 12, no. 1, pp. 55-67, 1970.
  • H. D. Vinod and A. Ullah, “Recent advances in regression methods”, Marcel Dekker, New York, Inc., 1981.
  • B. F. Swindel, “Good Ridge Estimators Based on Prior Information”, Communications in Statistics-Theory and Methods, vol. A5, pp. 1065-1075, 1976.
  • G. Trenkler, “Generalized mean squared error comparisons of biased regression estimators”, Communications in Statistics-Theory and Methods, vol. A9, no. 12, pp. 1247-1259, 1980.
  • J. L. Pliskin, “A ridge type estimator and good prior means”, Communications in Statistics-Theory and Methods, vol. 16, no. 12, pp. 3429–3437, 198.
  • A. E. Hoerl, R. W. Kennard and K. F. Baldwin, “Ridge regression: some simulations”, Communications in Statistics-Simulation and Computation, vol. 4, pp. 105–123, 1975.
  • B. M. G. Kibria, “Performance of some new ridge regression estimators”, Communications in Statistics-Simulation and Computation, vol. 32, no. pp. 419–435, 2003.
  • J. F. Lawless and P. A. Wang, “Simulation study of ridge and other regression estimators”, Communications in Statistics-Theory and Methods , vol. 5, no. 4, pp. 307-323, 1976.
  • W. E Griffiths, R.C. Hill and G.G. Judge, “Learning and Practicing Econometrics”, John Wiley&Sons Inc., New York, 1993.
Year 2018, Volume: 22 Issue: 6, 1631 - 1637, 01.12.2018
https://doi.org/10.16984/saufenbilder.377423

Abstract

References

  • A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, vol. 12, no. 1, pp. 55-67, 1970.
  • H. D. Vinod and A. Ullah, “Recent advances in regression methods”, Marcel Dekker, New York, Inc., 1981.
  • B. F. Swindel, “Good Ridge Estimators Based on Prior Information”, Communications in Statistics-Theory and Methods, vol. A5, pp. 1065-1075, 1976.
  • G. Trenkler, “Generalized mean squared error comparisons of biased regression estimators”, Communications in Statistics-Theory and Methods, vol. A9, no. 12, pp. 1247-1259, 1980.
  • J. L. Pliskin, “A ridge type estimator and good prior means”, Communications in Statistics-Theory and Methods, vol. 16, no. 12, pp. 3429–3437, 198.
  • A. E. Hoerl, R. W. Kennard and K. F. Baldwin, “Ridge regression: some simulations”, Communications in Statistics-Simulation and Computation, vol. 4, pp. 105–123, 1975.
  • B. M. G. Kibria, “Performance of some new ridge regression estimators”, Communications in Statistics-Simulation and Computation, vol. 32, no. pp. 419–435, 2003.
  • J. F. Lawless and P. A. Wang, “Simulation study of ridge and other regression estimators”, Communications in Statistics-Theory and Methods , vol. 5, no. 4, pp. 307-323, 1976.
  • W. E Griffiths, R.C. Hill and G.G. Judge, “Learning and Practicing Econometrics”, John Wiley&Sons Inc., New York, 1993.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Selma Toker 0000-0002-4557-1646

Nimet Özbay 0000-0003-3840-3107

Publication Date December 1, 2018
Submission Date January 11, 2018
Acceptance Date March 26, 2018
Published in Issue Year 2018 Volume: 22 Issue: 6

Cite

APA Toker, S., & Özbay, N. (2018). Evaluation of Two Stage Modified Ridge Estimator and Its Performance. Sakarya University Journal of Science, 22(6), 1631-1637. https://doi.org/10.16984/saufenbilder.377423
AMA Toker S, Özbay N. Evaluation of Two Stage Modified Ridge Estimator and Its Performance. SAUJS. December 2018;22(6):1631-1637. doi:10.16984/saufenbilder.377423
Chicago Toker, Selma, and Nimet Özbay. “Evaluation of Two Stage Modified Ridge Estimator and Its Performance”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1631-37. https://doi.org/10.16984/saufenbilder.377423.
EndNote Toker S, Özbay N (December 1, 2018) Evaluation of Two Stage Modified Ridge Estimator and Its Performance. Sakarya University Journal of Science 22 6 1631–1637.
IEEE S. Toker and N. Özbay, “Evaluation of Two Stage Modified Ridge Estimator and Its Performance”, SAUJS, vol. 22, no. 6, pp. 1631–1637, 2018, doi: 10.16984/saufenbilder.377423.
ISNAD Toker, Selma - Özbay, Nimet. “Evaluation of Two Stage Modified Ridge Estimator and Its Performance”. Sakarya University Journal of Science 22/6 (December 2018), 1631-1637. https://doi.org/10.16984/saufenbilder.377423.
JAMA Toker S, Özbay N. Evaluation of Two Stage Modified Ridge Estimator and Its Performance. SAUJS. 2018;22:1631–1637.
MLA Toker, Selma and Nimet Özbay. “Evaluation of Two Stage Modified Ridge Estimator and Its Performance”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1631-7, doi:10.16984/saufenbilder.377423.
Vancouver Toker S, Özbay N. Evaluation of Two Stage Modified Ridge Estimator and Its Performance. SAUJS. 2018;22(6):1631-7.