Abstract
This paper considers several estimators for estimating the biasing parameter in the study of partial linear models in the presence of multicollinearity. After exhibiting the MSE of ridge estimator based on eigenvalues of design matrix, a simulation study has been conducted to compare the performanceof the estimators. Based on the simulation studywe found that, increasing the correlation between the independent variables has positive effect on the MSE (signal-to-noise-ratio). However, increasingthe value of \(\rho \) has negative effect on MSE. When the sample size increases the MSE decreases even when the correlation between the independentvariables is large. An application of the proposed model is considered forhousing attributes to illustrate the performance ofdifferent estimators.
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References
Akdeniz F Akdeniz, Duran E (2009) Liu-type estimator in semiparametric regression model. J Stat Comput Simul. doi:10.1080/00949650902821699
Akdeniz F, Erol H (2003) Mean squared error matrix comparisons of some biased estimators in linear regression. Commun Stat Theory Method 32:2389–2413
Akdeniz F, Kaciranlar S (1995) On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE. Commun Stat Theory Method 24:1789–1797
Akdeniz F, Tabakan G (2009) Restricted ridge estimators of the parameters in semiparametric regression model. Commun Stat Theory Method 38:1852–1869
Akdeniz Duran E, Akdeniz F (2012) Efficiency of the modified jackknifed Liu-type estimator. Stat Pap 53:265–280
Akdeniz Duran E, Akdeniz F, Hu H (2011) Efficiency of a Liu-type estimator in semiparametric regression models. J Comp Appl Math 235:1418–1428
Engle RF, Granger CWJ, Rice J, Weiss A (1986) Semiparametric estimates of the relation between weather on electricity sales. J Am Stat Assoc 81:310–320
Eubank RL, Kambour EL, Kim JT, Klipple K, Reese CS, Schimek MG (1998) Estimation in partially linear models. Comput Stat Data Anal 29:27–34
Gibbons DG (1981) A simulation study of some ridge estimators. J Am Stat Assoc 76:131–139
Green PJ, Silverman BW (1994) Nonparametric regression and generalized linear model. Chapman and Hall, New York
Hastie T, Tibshirani R (1986) Generalized additive model. Stat Sci 1:297–318
Hocking RR, Speed FM, Lynn MJ (1976) A class of biased estimator in linear restriction in linear regression model with non-normal disturbance. Commun Stat A25:2349–2369
Horel AE, Kennard RW (1970) Ridge regression: biased estimation for non-orthogonal problems. Thechnometrics 12:69–82
Horel AE, Kennard RW (1975) Ridge regression: some simulation. Commun Stat 4:105–123
Hu H (2005) Ridge estimation of semiparametric regression model. J Comput Appl Math 176:215–222
Inan D (2013) Combining the Liu-type estimator and the principal component regression estimator. Pap Stat. doi:10.1007/s00362-013-0571-5
Kibria BMG (1996) On preliminary test ridge regression estimators for linear restriction in a regression model with non-normal disturbances. Commun Stat Theory Method 25:2349–2369
Kibria BMG (2003) Performance of some new ridge estimation. Commun Stat Simul Co 32:419–435
Kibria BMG (2012) Some Liu and Ridge type estimators and their properties under the Ill-conditioned Gaussian linear regression model. J Stat Comput Simul 82:1–17
Kibria BMG, Saleh K Md, E (2012) Improving the estimators of the parameters of a probit regression model: a ridge regression approach. J Stat Plan Inference 142:1421–1435
Kristofer M, Kibria BMG, Shukur G (2012) On Liu estimators for the logit regression model. Econ Model 29:1483–1488
Lawless JF, Wang P (1976) A simulation study of ridge and other regression estimators. Commun Stat Theory Method 5:307–323
Li Y, Yang H (2012) A new Liu-type estimator in linear regression model. Stat Pap 53:427–437
Li Y, Yang H (2010) A new stochastic mixed ridge estimator in linear regression model. Stat Pap 51:315–323
Liu K (1993) A new class of biased estimate in linear regression. Commun Stat Theory Method 22:393–402
McDonald GC, Galarneau DI (1975) A monte carlo evaluation of some Ridge- type estimators. J Am Stat Assoc 70:407–416
Ozkale MR (2009) Comment on Ridge estimation to the restricted linear model. Commun Stat Theory Method 38:1094–1097
Ozkale MR, Kaciranlar S (2007) The restricted and unrestricted two parameter estimators. Commun Stat Theory Method 36:2707–2727
Rahakrishna Rao C, Toutenburg H (1995) Linear models: least squares and alternatives. Springer, Baldwin
Roozbeh M, Arashi M (2013) Feasible ridge estimator in partially linear models. J Mult Anal 116:35–44
Roozbeh M, Arashi M, Niroomand HA (2011) Ridge regression methodology in partial linear models with correlated errors. J Stat Comput Simul 81:517–528
Saleh AK, Md E (2006) Theory of preliminary test and Stein-type estimation with applications. Wiley, New York
Saleh K Md E, Kibria BMG (2011) On some Ridge regression estimators: a nonparametric approach. J Nonparametr Stat 23:819–851
Schimek MG (2000) Estimation and inference in partially linear models with smoothing spline. J Stat Plan Inference 91:525–540
Speckman P (1988) Kernel smoothing in partial linear models. J R Stat Soc Ser B 50:413–436
Swindel BF (1976) Good Ridge estimators based on prior information. Commun Stat Theory Method 5:1065–1075
Zeebari Z, Shukur G, Kibria BMG (2012) Modified Ridge parameters for seemingly unrelated regression model. Commun Stat Theory Method 41:1675–1691
Zhong Z, Yang H (2007) Ridge estimation to the restricted linear model. Commun Stat Theory Method 36:2099–2115
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The authors would like to thank three anonymous reviewers for careful reading and useful comments which improved the quality and presentation of the paper greatly.
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Arashi, M., Valizadeh, T. Performance of Kibria’s methods in partial linear ridge regression model. Stat Papers 56, 231–246 (2015). https://doi.org/10.1007/s00362-014-0578-6
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DOI: https://doi.org/10.1007/s00362-014-0578-6