Analysis of semi-parametric single-index models by using MAVE-method based on some kernel functions

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper, we used many forms of kernel functions with minimum average variance estimation (MAVE) method [Xia2002] we called the proposed methods (MAVE-Biweight), (MAVE-Epanechnikov ) and .(MAVE-Gaussian ) for estimation the parameters and the link function of the single – index model (SIM) comparing with other methods of estimation . to evaluate the performing of the various methods s simulation and a real data have been used, conclusions showed that the (MAVE- Gaussian) method in this paper gave better results compared with other methods depending on the mean squared error (MSE) and mean Absolute error (MAE) criterion for comparison.


  • Keywords


    Single-Index Model; MAVE Method; Kernel Function; Bandwidth Parameter; Curse of Dimensionality.

  • References


      [1] Al – kenani, A., and Yu, K. (2013), “Penalized single Indexquantile regression “. International Journal of statistics and probability, vol.2, No.3, pp. 12-30.

      [2] Akkus, O. (2011), “Xplore package for the popular parametric and semi-parametric single index models " .Journe of science ,vol.24 , No.4, pp. 753-762 .

      [3] Hansen, W.E. (2009),"lecture Notes on Non-parametric ".university of Wisconsin,spring.

      [4] Hardle, W., Hall, P., and Ichimura, H. (1993)," optimal smoothing in single index models “. The Annals of statistics, vol.21, pp. 157-178. https://doi.org/10.1214/aos/1176349020.

      [5] Kong, E., Xia, Yi. (2007), “variable selection for the single index model“.Biometrika94,pp.217-229. https://doi.org/10.1093/biomet/asm008.

      [6] Kopytou, E., and Santalova, D. (2007), “Application of the single index model for forcasting of the inland conveyances “Recent advances in stochastic modeling and data analysis. Singupre, world scientific poblishing copte Ltd,pp.268-276. https://doi.org/10.1142/9789812709691_0033.

      [7] Lai, P., Wang, Q., and Lion, H. (2011), “Bias-corrected GEE estimation and smooth–threshold GEE variable selection for single index models with clustered data “. Journal of multivariate analysis, vol.105,No.1,pp.422-432. https://doi.org/10.1016/j.jmva.2011.08.009.

      [8] Leng, C.L., Xia, Y., & Xu, J. (2008), “An adaptive estimation method for semi-parametric models and dimension reduction “. Department of statistics and Applied probability National university of Singapore .Exploration of a nonlinear world, pp. 347-360.

      [9] Li , R. , and Fan , J., (2004) , " New Estimation and model selection procedures for semi-parametric modeling in longitudinal Data A nalysis " , journal of the American statistical Association , vol .99 , No . 467, pp. 710-723.

      [10] Naik, P.A., and Tsai, C.L. (2001), "single index model selections". Biometrika88,pp.821-832. https://doi.org/10.1093/biomet/88.3.821.

      [11] Peng, H., and Huang, T. (2011), “penalized least squares for single index models “. Journal of statistical planning and inference 141, pp. 1362-1379. https://doi.org/10.1016/j.jspi.2010.10.003.

      [12] Thomas, J.F. (2006), “Simulation study for single index model" .submitted to the Department of Mathematical sciences of Clemson University, in partial fulfillment for The requirements for The degree of Master of science in Mathematical sciences.

      [13] Wang, G. (2015),"High / Ultra High Dimensional single – index models ". A Dissertation submitted to The Graduate Faculty of The University of Georgina in partial Fulfillment of The requirements for the Doctor PHD. Department of statistics, Athens, GEORGIA.

      [14] Wang ,Q.,Zhang,T.,and Hardle,W.,(2014), " An Extended single – index model with missing response at random " . SFB 649, Humbodt, university Zu Berlin spandaure. http:// sfb649.wiwi.hu-berlin .de.

      [15] Wang, T., Xu .P.,and Zhu , L.(2013) ," Penalized Minimum Average Variance Estimation " . Statistics sinica 23, pp.543-569. https://doi.org/10.5705/ss.2011.275.

      [16] Xia, Y. (2006), "Asymptotic Distribution for Tow estimators of the Single – index model”, National university of singopore, EconometricTheory,22,pp.1112–1137. https://doi.org/10.1017/S0266466606060531.


 

View

Download

Article ID: 7258
 
DOI: 10.14419/ijasp.v5i1.7258




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.