TY - JOUR TT - A STUDY ON TESTS OF HYPOTHESIS BASED ON RIDGE ESTIMATOR AU - Gökpınar, Esra AU - Ebegil, Meral PY - 2016 DA - December JF - Gazi University Journal of Science PB - Gazi University WT - DergiPark SN - 2147-1762 SP - 769 EP - 781 VL - 29 IS - 4 KW - Biasing factors KW - Ridge regression KW - Hypothesis testing KW - Type I error KW - Power of test N2 - The literature of Ridge regression include many articles that deal with point estimation of the coefficients vector . However, few of them tackle the statistical inference problem about or some of its components. One of them is introduced by Halawa and Basuiouni[1] who present non-exact tests based on Ridge regression by using two different biasing parameters (k) which are proposed by Hoerl and Kennard [2] and Hoerl et al. [3]. Thus, we investigate others popular k values used the Ridge regression for testing significance of regression coefficients. We compare tests in terms of type I error rates and powers by using Monte Carlo simulation. In addition, a real data example is presented. CR - A.M. Halawa and M.Y.E. Basuiouni, “Tests of CR - Regression Coefficients under Ridge Regression CR - Models”, Journal of Statistical Computation and CR - Simulation, 65, 2000, pp. 341-356. CR - A.E. Hoerl and R.W. Kennard, “Ridge regression: CR - biased estimation for non-orthogonalproblems”, CR - Technometrics,12, 1970, pp. 55–67. CR - A.E. Hoerl, R.W. Kennard and K.F. Baldwin, “Ridge CR - regression: some simulation”, Communications in CR - Statistics, 5, 1975,pp. 105–123. CR - C.M. Theobald, “Generalizations of Mean Square CR - Error Applied to Ridge Regression”, Journal of the CR - Royal Statistical Society. Series B CR - (Methodolojical), 36, 1974,pp.103-106. CR - J.F. Lawless and P. Wang, “A Simulation Study of CR - Ridge and Other Regression Estimators”, CR - Communications in Statistics: Theory and CR - Methods,7, 1976, pp. 139-164. CR - A.P. Dempster, M. Schatzoff and N. Wermuth, “A CR - Simulation Study of Alternatives to Ordinary Least CR - Squares”, Journal of the American Statistical CR - Association, 72, 1977,pp. 77-91. CR - D.G. Gibbons, “A Simulation Study of Some Ridge CR - Estimators”, Journal of the American Statistical CR - Association, 76, 1981,pp.131-139. CR - A. K. Md. E. Saleh and B.M.G. Kibria, CR - “Performances of Some New Preliminary Test CR - Ridge Regression Estimators and Their Properties”, CR - Communicationsin Statistics: Theory and Methods, CR - , 1993,pp. 2747-2764. CR - B.M.G. Kibria, “Performance of Some New Ridge CR - Regression Estimators”, Communications in CR - Statistics: Simulation and Computation, 32, CR - ,pp. 419-435. CR - G. Khalaf and G. Shukur, “Choosing Ridge CR - Parameters for Regression Problems”, CR - Communications in Statistics: Theory and Methods, CR - , 2005,pp.1177-1182. CR - J. Zhang and M. Ibrahim, “A Simulation Study on CR - SPSS Ridge Regression and Ordinary Least CR - Squares Regression Procedures for Multicolliearity CR - data”, Journal of Applied Statistics, 32, 2005,pp. CR - -588. CR - A.K.Md.E. Saleh, “Theory of Preliminary Test and CR - Stein-Type Estimation with Applications”, Wiley, CR - New York, 2006. CR - M. Alkhamisi, G. Khalaf and G. Shukur, “Some CR - Modifications for Choosing Ridge Parameters”, CR - Communications in Statistics-Theory and Methods, CR - , 2006,pp. 2005-2020. CR - M. Alkhamisi and G. Shukur, “Developing Ridge CR - Parameters for SUR Model”, Communications in CR - Statistics -Theory and Methods, 37, 2008,pp. 544- CR - G. Muniz and B.M.G. Kibria, “On Some Ridge CR - Regression Estimators: An Empirical CR - Comparisons”, Communications in Statistics- CR - Simulation and Computation, 38, 2009,pp. 621- CR - F. Gökpınar and M. Ebegil, “A Comparative Study CR - on Ridge Estimators in Regression Problems”, CR - Journal of SainsMalaysiana, 2014 (in submission). CR - E.P. Liski, “A Test of the Mean Square Error CR - Criterion for shrinkage Estimators”, CR - Communications in Statistics: Theory and Methods, CR - , 1982,pp. 543-562. CR - E.P. Liski, “Choosing a shrinkage Estimator-a test CR - of the Mean Square Error Criterion”, Proc. First CR - Tampere Sem. Linear Models, 1983,pp. 245-262. CR - R.L. Obenchain, “Classical F-Tests and Confidence CR - Regions for Ridge Regression”, Technometrics, 19, CR - , pp. 429-439. CR - D. Coutsourides and C.G. Troskie, “F and t Tests CR - for a General Class of Estimators”, South African CR - Statistical Journal, 13, 1979,pp. 113-119. CR - A. Ullah, R.A.L. Carter and V.K. Srivastova, “The CR - Sampling Distribution of Shrinkage Estimators and CR - their F Ratio in Regression Model”, Journal of CR - Econometrics, 25, 1984,pp. 109-122. CR - M. Karakuş, A. Bayrak, E. Çalıkoğlu and M. CR - Kıralan, “Comparison of oxidation stability of CR - virgin olive oils from different locations of CR - Turkey”, ActaAlimentaria, 43, 2014, pp. 133-141. CR - H.Woods, H.H. Steinour, and H.R. Starke, “Effect CR - of composition of Portland cement on heat evolved CR - during hardening, Ind. Eng. Chem.”, 24, 1932, pp. CR - –1214. CR - M. Ebegil, F. Gökpınar, “A Test Statistic to Choose CR - Between Liu-Type and Least Squares Estimator CR - Based on Mean Square Error Criteria”, Journal of CR - Applied Statistics, 39(10), 2012, pp. 2081-2096. UR - https://dergipark.org.tr/en/pub/gujs/issue//289687 L1 - https://dergipark.org.tr/en/download/article-file/273151 ER -