Semi-parametric nonlinear regression and transformation using functional networks

Computational Statistics and Data Analysis

Volumn 52, Issue 4, 2008, Pages 2129-2157

  Castillo, Enrique ^a   Hadi, Ali S ^b   Lacruz, Beatriz ^c   Pruneda, Rosa E ^d  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b AMERICAN UNIVERSITY IN CAIRO   (Egypt)

^c UNIVERSITY OF ZARAGOZA   (Spain)

^d UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Adjusted correlation coefficient; Akaike information criterion; Alternating conditional expectation; Canonical correlation; Constrained least squares; Minimum description length measure; Transforming both sides

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; NEURAL NETWORKS; NONLINEAR ANALYSIS; PROBLEM SOLVING; TOPOLOGY;

AKAIKE INFORMATION CRITERION; ALTERNATING CONDITIONAL EXPECTATIONS; CANONICAL CORRELATIONS; CONSTRAINED LEAST SQUARES; EXPLANATORY VARIABLES; FUNCTIONAL EQUATIONS; FUNCTIONAL NETWORKS; MINIMUM DESCRIPTION LENGTH MEASURES; OPTIMAL TRANSFORMATIONS; TRANSFORMING BOTH SIDES;

REGRESSION ANALYSIS;

EID: 35748932397     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.07.006     Document Type: Article

References (24)

1. Aczél J. Lectures on Functional Equations and their Applications, Mathematics in Science and Engineering vol. 19 (1966), Academic Press, New York
2. Atkinson A.C. Plots, Transformations, and Regression (1985), Clarendon Press, Oxford
3. Breiman L., and Friedman J.H. Estimating optimal transformations for multiple regression and correlation (with discussions). J. Amer. Statist. Assoc. 80 391 (1985) 580-619
4. Breiman L., Friedman J.H., Olshen R., and Stone C.J. Classification and Regression Trees (1993), Chapman & Hall, New York
5. Carroll R.J., and Ruppert D. Transformations and Weighting in Regression (1988), Chapman & Hall, New York
6. Castillo E. Functional networks. Neural Process. Lett. 7 (1998) 151-159
7. Castillo E., and Gutiérrez J.M. Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos. Phys. Lett. A 244 (1998) 71-84
8. Castillo E., and Ruiz-Cobo R. Functional Equations in Science and Engineering (1992), Marcel Dekker, New York
9. Castillo E., Cobo A., Gutiérrez J.M., and Pruneda E. An Introduction to Functional Networks with Applications (1998), Kluwer Academic Publishers, New York
10. Castillo E., Cobo A., Gutiérrez J.M., and Pruneda E. Working with differential, functional and difference equations using functional networks. Appl. Math. Modeling 23 (1999) 89-107
11. Castillo E., Cobo A., Gómez-Nesterkín R., and Hadi A.S. A general framework for functional networks. Networks 35 (2000) 70-82
12. Castillo E., Gutiérrez J.M., Hadi A.S., and Lacruz B. Some applications of functional networks in statistics and engineering. Technometrics 43 (2001) 10-24
13. Castillo E., Iglesias A., and Ruiz-Cobo R. Functional Equations in Applied Sciences. Mathematics in Science and Engineering vol. 199 (2005), Elsevier, Amsterdam
14. Fox J. Multiple and Generalized Nonparametric Regression (2000), Sage Publications, Inc., Beverley Hills, CA
15. Friedman J.H. Multivariate adaptive regression splines. Ann. Statist. 19 1 (1991) 1-141
16. Friedman J.H., and Stuetzle W. Projection pursuit regression. J. Amer. Statist. Assoc. 76 (1981) 817-823
17. Harrison D., and Rubinfeld D.L. Hedonic housing prices and the demand for clean air. J. Environ. Econom. Manage. 5 (1978) 81-102
18. Hastie T.J., and Tibshirani R.J. Generalized Additive Models (1990), Chapman & Hall, London
19. Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. third ed (1999), Springer, Berlin
20. Pace R.K. Nonparametric methods with application to hedonic models. J. Real Estate Finance Econom. 7 3 (1993) 185-204
21. Peixoto J.L. A property of well-formulated polynomial regression models. Amer. Statist. 44 (1990) 26-30
22. Ryan B.F., and Joiner B.L. MINITAB Handbook. third ed (1994), Duxbury Press
23. Sockett E.B., Daneman D., Clarson C., and Ehrich R.M. Factors affecting and patterns of residual insulin secretion during the first year of type I (insulin dependent) diabetes mellitus in children. Diabetes 30 (1987) 453-459
24. Tibshirani R.J. Estimating optional transformations for regression via additivity and variance stabilization. J. Amer. Statist. Assoc. 83 (1988) 394-405