Araştırma Makalesi
BibTex RIS Kaynak Göster

Estimation in Semiparametric Regression Models

Yıl 2010, Cilt: 7 Sayı: 2, 1 - 10, 15.12.2010

Fikri Akdeniz

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • 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 Ph D. Thesis, Gazi University, Ankara (unpublished).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.

Yarı Parametrik Regresyon Modellerinde Tahmin Etme

Yıl 2010, Cilt: 7 Sayı: 2, 1 - 10, 15.12.2010

Fikri Akdeniz

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Araştırma Makaleleri
Yazarlar

Fikri Akdeniz

Yayımlanma Tarihi 15 Aralık 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 7 Sayı: 2

Kaynak Göster

APA Akdeniz, F. (2010). Estimation in Semiparametric Regression Models. İstatistik Araştırma Dergisi, 7(2), 1-10.
 Kapak Resmi İndir