Relationship between Sums of Squares in Linear Regression and Semi-parametric Regression

Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076516

References:

[1] Mayers, Raymond. H., Classical and Modern Regression with Applications, Duxbury Classical Series, United States, 1990.
[2] Montgomarey, C. Douglas., Peck, A. Elizabeth., Vining, G. Geoffrey., Introduction to Linear Regression Analysis, John Wiley&Sons,Inc., Toronto, 2001.
[3] Hardle, Wolfang., M├╝ller, Marlene., Sperlich, Stefan., Weratz, Axel., Nonparametric and Semiparametric Models, Springer, Berlin, 2004.
[4] Eubank, R. L., Nonparametric Regression and Smoothing Spline, Marcel Dekker Inc., 1999
[5] Wahba, G., Spline Model for Observational Data, Siam, Philadelphia Pa., 1990.
[6] Green, P.J. and Silverman, B.W., Nonparametric Regression and Generalized Linear Models, Chapman & Hall, 1994.
[7] Schimek, G. Michael, Estimation and Inference in Partially Linear Models with Smoothing Splines, Journal of Statistical Planning and Inference, 91, 525-540, 2000.
[8] Hastie, T.J. and Tibshirani, R.J., Generalized Additive Models, Chapman & Hall /CRC, 1999.
[9] Wood, N. Simon., Generalized Additive Models An Introduction With R, Chapman & Hall/CRC, New York, 2006.
[10] Hastie, T., The gam Package, Generalized Additive Models, R topic documented, http://cran.r.project.org/packages/gam.pdf, February 16, 2008.