XploRe Package for the Popular Parametric and the Semiparametric Single Index Models

Abstract

This study introduces and shows the applicability of the XploRe commands of the parametric and the semiparametric single index models, which are two most popular alternatives of each other. The commands required for the estimation in all stages of the semiparametric estimation and the parametric logistic, probit and complementary log log regression models are introduced in detail. An artificial data set is used to demonstrate the applicability of the commands in practice. The major contribution of this study is that it enables researchers to obtain additional outputs in easier way that are not so easy to have in the standard statistical packages especially for the semiparametric models. Additionally, users could extend and adapt these commands in conjunction with the new developments in this area.  

 

 

Key Words:  Single index model, Semiparametric approach, Binary response modelling, XploRe.                       

Keywords

• Single index model, Semiparametric approach, Binary response modelling, XploRe.

References

1. Aldrich, J.H., Nelson, F.D., “Linear Probability, Logit and Probit Models”, Sage Publications, London (1984).
2. Hardle, W., Müller, M., Sperlich, S., Werwatz, A., “Nonparametric and Semiparametric Models”, Springer-Verlag, New York (2004).
3. Hardle, W., “Applied Nonparametric Regression”, Cambridge University Press, Cambridge (1990).
4. Hardle, W., Klinke, S., Müller, M., “XploRe Learning Guide”, MDtech, Springer-Verlag, New York (1999).
5. Hardle, W., Hlavka, Z., Klinke, S., “XploRe Application Guide”, e-book, MD Tech, Springer-Verlag, New York (2003).
6. Hardle, W., Klinke, S., Turlach, B.A., “XploRe: An Interactive Statistical Computing Environment: Statistics and Computing”, Springer-Verlag, New York (2007).
7. Horowitz, J.L., “Semiparametric Methods in Econometrics”, Springer-Verlag, New York (1998).
8. Hosmer, D.W., Lemeshow, S., “Applied Logistic Regression”, John Wiley and Sons, New York (1989).

9. Manski, C. F., “Identification of binary response models”, Journal of the American Statistical Association, 83: 729-738 (1988).
10. McCullagh, P., Nelder, J.A., “Generalized
11. Linear Models: Monographs on Statistics and Applied Probability 37”, Chapman and Hall, London (1989).
12. Nadaraya, E.A., “On estimating regression”, Theory of Probability and its Applications, 10: 186-190 (1964).
13. Powell, J.L., Stock, J.H., Stoker, T.M.,
14. “Semiparametric estimation of index coefficients”, Econometrica, 57(6): 1403-1430 (1989).
15. Proença, I., Werwatz, A., “Comparing parametric and semiparametric binary response models”, Humboldt University, Series: Sonderforschungsbereich 373, Number: 1995- 36, Berlin, (1994).
16. Watson, G.S., “Smooth regression analysis”, Sankhya, 26(A): 359-72 (1964).