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Journals / Gazi University Journal of Science / 2024 / Volume: 37 Issue: 4

Testing the Significance of Regression Coefficients in Liu Type Estimators

Hilal Kaplan Tabak(GAZI UNIVERSITY, INSTITUTE OF SCIENCE)0000-0001-7842-2535
Meral Ebegil(GAZI UNIVERSITY, FACULTY OF SCIENCE)0000-0003-4798-3422
Esra Gökpınar(GAZI UNIVERSITY, FACULTY OF SCIENCE)0000-0003-2148-4940
Pages
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Publication Date
2024-12-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, a real data application is performed to better understand the test procedure.

📌 3 Key Takeaways

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Objective & Hypothesis:In the linear regression model, the multicollinearity problem arises when there is a linear relationship between independent variables.
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Key Findings & Data:This situation causes the variance of the estimations of the model parameters obtained by the Least Squares Estimator method to increase and move away from the true value, resulting in unstable and incorrect results.
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Conclusion & Impact:In addition, a real data application is performed to better understand the test procedure.
🔬Design:Modeling & Simulation
📍Scope:2000 Verileri
⚙️Variables:Biased estimators · Hypothesis testing · Multicollinearity

Abstract

In the linear regression model, the multicollinearity problem arises when there is a linear relationship between independent variables. This situation causes the variance of the estimations of the model parameters obtained by the Least Squares Estimator method to increase and move away from the true value, resulting in unstable and incorrect results. Biased Estimator methods are developed to eliminate the adverse effects caused by multicollinearity. In this study, a test statistic is obtained to test the significance of the model coefficients for the Liu-Type Estimator using the test statistic method suggested in the study of Halawa and El-Bassiouni (2000). With a simulation study, the significance of the model coefficients of the Ridge, Liu, and Liu type biased estimators in different situations is tested; the type I errors and power values of the estimators are calculated; the results are compared. In addition, a real data application is performed to better understand the test procedure.

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Cite This Article

Tabak, H. K., Ebegil, M., Gökpınar, E. (2024). Testing the Significance of Regression Coefficients in Liu Type Estimators. Gazi University Journal of Science, Volume: 37 Issue: 4. https://doi.org/10.35378/gujs.1360997

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References (19)

  1. Hoerl, A.E., Kennard, R.W., “Ridge regression. Biased estimation for nonorthogonal problems”, Technometrics, 12: 55–67, (1970).
  2. Liski, E.P., “A test of the mean square error criterion for shrinkage estimators”, Communications in Statistics, 11(5): 543-562, (1982).
  3. Liu, K., “A new class of biased estimate in linear regression”, Communications in Statistics. Theory and Methods, 22(2): 393-402, (1993).
  4. Akdeniz, F., Kaçıranlar, S., “On the almost unbiased generalized liu estimator and unbiased estimation of the bias and MSE”, Communications in Statistics-Theory and Methods, 24(7): 1789-179, (1995).
  5. Halawa, A.M., Bassiouni, M.Y., “Tests of regression coefficients under ridge regression models”, Journal of Statistical Simulation and Computation, 65: 341-56, (2000).
  6. Kibria, B.M.G., “Performance of some new ridge regression estimators”, Simulation and Computation, 32(2): 419-435, (2003).
  7. Liu, K., “Using liu-type estimator to combat collinearity”, Communications in Statistics, 32(5): 1009-1020, (2003).
  8. Ebegil, M., Gökpınar, F., Ekni, M., “A simulation study on some shrinkage estimators”, Hacettepe Journal of Mathematics and Statistics, 35: 213–226, (2006).
  9. Liski, E.P., “ Choosing a shrinkage estimator a test of the mean square error criterion”, Proc. First Tampere Sem. Linear Models, 245-262, (1983).
  10. Özkale, M.R., Kaçıranlar, S., “Superiority of the r-d class estimator over some estimators by the mean square error matrix criterion”, Stattistics and Probability Letters, 77: 438–446, (2007).
  11. Sakallıoğlu, S., Kaçıranlar, S., “A new biased estimator based on ridge estimation”, Statistical Papers, 49: 669-689, (2008).
  12. Ebegil, M., Gökpınar, F., “A test statistic to choose between liu-type and least squares estimator based on mean square error criteria”, Journal of Applied Statistics, 39(10): 2081-2096, (2012).
  13. Gökpınar, E., Ebegil, M., “A study on tests of hypothesis based on ridge estimator”, Gazi University Journal of Science, 29(4): 769-781, (2016).
  14. Wilcox, R.R., “Multicolinearity and ridge regression: results on type I errors, power and heteroscedasticity”, Journal of Applied Statistics, 46(5): 946-957, (2019).
  15. Melo, S.P., Kibria, B.M.G., “Testing the regression coefficients in the liu linear regression model: simulation and application”, International Journal of Statistical Analysis, 2(1): 55-68, (2021).
  16. Hald, A., “Statistical Theory with Engineering Applications”, New York: Wiley, (1952).
  17. Hoerl, A.E., Kennard, R.W., Baldwin, K.F., “Ridge regression. Some simulation”, Communications in Statistics, 5: 105–123, (1975).
  18. McDonald, G., Galarneau, D., “A monte carlo evaluation of some ridge-type estimators”, Journal of the American Statistical Association, 70 (350): 407-416, (1975).
  19. Bradley, J.V., “Robustness?”, British Journal of Mathematical and Statistical Psychology, 31:144-152, (1978).