A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and applicable in practical fields.
@article{bwmeta1.element.bwnjournal-article-amcv17i2p179bwm,
author = {Hu, Shaolin and Meinke, Karl and Chen, Rushan and Huajiang, Ouyang},
title = {Iterative estimators of parameters in linear models with partially variant coefficients},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {17},
year = {2007},
pages = {179-187},
zbl = {1119.93413},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p179bwm}
}
Hu, Shaolin; Meinke, Karl; Chen, Rushan; Huajiang, Ouyang. Iterative estimators of parameters in linear models with partially variant coefficients. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) pp. 179-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p179bwm/
[000] Brown D.C. (1964): The Error Model Best Estimation Trajectory. - Tech. Rep. AD 602799: http://stinet.dtic.mil/oai/oai?&verb=getRecorg&metadataPrefix=html&identifier=AD0602799
[001] Dodge Y. and Kova J. (2000): Adaptive Regression. - Berlin: Springer.
[002] Draper N.R. and Smith H. (1981): Applied Regression Analysis. - New York: Wiley. | Zbl 0548.62046
[003] Eubank R., Chunfeng H., Maldonado Y., Naisyin W., Suojin W., Buchanan R.J. (2004): Smoothing spline estimation in varying coefficient models. - J. Roy. Stat. Soc. B, Vol.66, No.3, pp.653-667. | Zbl 1046.62033
[004] Fahrmeier L. and Tutz G.(2001): Multivariate Statistical Modeling Based on Generalized Linear Models. - Berlin: Springer.
[005] Frank E. and Harrell J.(2002): Regression Modeling Strategies with Applications to Linear Models, Logistic Regression, and Survival Analysis. - New York: Springer. | Zbl 0982.62063
[006] Graybill F.A. and Iyer H.K. (1994): Regression Analysis: Concepts and Applications. - Massachusetts: Duxbury Press. | Zbl 0868.62056
[007] Hu Shaolin and Sun Guoji (2001): Process Monitoring Technique and Applications. - Bejing: National Defense Industry Press.
[008] Kala R. and Kłaczyński K. (1988): Recursive improvement of estimates in a Gauss-Markov model with linear restrictions. Canad. J. Stat., Vol.16, No.3, pp.301-305. | Zbl 0667.62050
[009] Rencher A. (2000): Linear Models in Statistics. - New York: Wiley | Zbl 0943.62061