Estimation in Semiparametric Regression Models

Year 2010, Volume: 7 Issue: 2, 1 - 10, 15.12.2010

Fikri Akdeniz

Abstract

In this paper we consider the semiparametric regression model, y=Xß+ƒ+ε. We introduce a Liu-type estimator (LTE) in a semiparametric regression model. We obtained the semiparametric restricted ridge regression and Liu-type estimators for the parametric component in semiparametric regression model. We also introduced difference-based ridge regression and Liu-type estimators in semiparametric regression model. Difference-based estimator and difference-based Liu-type estimator are compared in the sense of mean-squared error criterion.

Keywords

Difference-based estimator, Differencing matrix, Liu-type estimator, Ridge estimator, Multicollinearity, Semiparametric regression model

Yarı Parametrik Regresyon Modellerinde Tahmin Etme

Abstract

Bu makalede y=Xß+ƒ+ε yarı parametrik regresyon modeli düşünüldü; yarı parametrik regresyon modelinde Liu-tip tahmin edici (LTE) önerildi. Ayrıca, yarı parametrik regresyon modelinde parametrik bileşen için yarı parametrik kısıtlı ridge regresyon ve Liu-tip tahmin edicileri de tanıtıldı. Farka dayalı tahmin edici ve farka dayalı Liu-tip tahmin edici hata kareleri ortalaması ölçütüne göre karşılaştırıldı.

Keywords

Farka dayalı tahmin edici, Fark alma matrisi, Liu-tip tahmin edici, Ridge tahmin edici, Çoklu içilişki, Yarı parametrik regresyon modeli

References

• Akdeniz D. E., 2010. Ph D. Thesis, Gazi University, Ankara (unpublished).
• Akdeniz, F., Kaçıranlar, S., 1995. On the almost unbiased generalized Liu estimator and unbiased estimation of the Bias and MSE. Commun. Statist.-Theory and Meth. 24(7), 1789-1797.
• Akdeniz, F., Tabakan, G., 2009. Restricted ridge estimators of the parameter in semiparametric regression model. Communications in Statistics- Theory and Methods 38(11):1852-1869.
• Akdeniz, F., Akdeniz D. E., 2010. Liu–type estimator in semiparametric regression models. Journal of Statistical Computation and Simulation 80(8):853-871.
• Akdeniz D. E., Akdeniz, F., 2010. Efficiency of Modified Jacknife Liu-type estimator. Statistical Papers DOI: 10.1007/s00362-010-0334-5).
• Akdeniz D, E., Akdeniz, F., Hongchang Hu., 2011. Efficiency of estimators in semiparametric regression models. Journal of Computational and Applied Mathematics 235:1418-1428.
• Buja, A., Hastie, T., Tibshirani, R., 1989. Linear smoothers and additive models. The Annals of Statististics, 17(2):453-555.
• Engle, R. F., Granger, C. W. J., Rice, J., Weiss, A., 1986. Semiparametric estimates of the relation between weather and electricity sales. J. Amer, Statist. Assoc. 81:310-320.
• Eubank, R. L., 1999. Nonparametric regression and Spline Smoothing. Marcel Dekker, New York.
• Eubank, R. L., Kambour, E. L., Kim, J. T., K.Klipple, K., Reese , C. S., Schimek, M.G., 1998. Estimation in partially linear models. Computational Statistics and Data Analysis 29:27-34.
• Green, P. J., Silverman, B. W., 1994. Nonparametric Regression and Generalized Linear Models. Chapman and Hall, New York.
• Gross, J., 2003. Restricted ridge estimation. Statistics and Probability Letters 65:57-64.
• Härdle, W., Liang, H., Gao, J., 2000. Partially Linear Models Springer-Verlag Co., New York.
• Härdle, W., Müler, M., Sperlich, S., Werwatz, A., 2004. Nonparametric and Semiparametric Models. Springer, New York.
• Hoerl, A. E., Kennard, R.W., 1970. Ridge regression: biased estimation for orthogonal problems. Technometrics 12:55-67.
• Liu, K. J., 1993. A new class of biased estimate in linear regression. Communications in Statistics–Theory and Methods 22:393-402.
• Przystalski, M., Krajewski, P., 2007. Constrained estimators of treatment parameters in semiparametric models. Statistics and Probability Letters 77(10):914-919.
• Rice, J. A., 1986. Convergence rates for partially spline models. Statistics and Probability Letters 4:203-208.
• Schimek, M. G., 2000. Estimation and inference in partially linear models with smoothing splines. Journal of Statistical Planning and Infrence 91:525-540.
• Speckman, P., 1988. Kernel somoothing in partial linear models. J. Roy, Statist.Soc.Ser. B. 50(3):413-436.
• Tabakan, G., Akdeniz, F., 2010. Difference –based ridge estimator of parameters in partial linear model. Stat. Papers, 357-368.
• Yatchew, A., 2003. Semiparametric Regression for the Applied Econometrician. Cambridge University Press.