Abstract
Nonparametric models have become more and more popular over the last two decades. One reason for their popularity is software availability, which easily allows to fit smooth but otherwise unspecified functions to data. A benefit of the models is that the functional shape of a regression function is not prespecified in advance, but determined by the data. Clearly this allows for more insight which can be interpreted on a substance matter level.
This paper gives an overview of available fitting routines, commonly called smoothing procedures. Moreover, a number of extensions to classical scatterplot smoothing are discussed, with examples supporting the advantages of the routines.
Keywords
- Unemployment Rate
- Generalize Additive Model
- Smoothing Parameter
- Nonparametric Regression
- Royal Statistical Society
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akaike, H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics22 203–217.
Akritas, M., Politis, D. (2003). Recent Advances and Trends in Nonparametric Statistics. North Holland, Amsterdam.
Bowman, A.W., Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.
Chiarella, C, Flaschel, P. (2000). The Dynamics of Keynesian Monetary Growth: Macro Foundations. Cambridge University Press, Cambridge.
Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Association, Series B34 187–220.
Crainiceanu, C, Ruppert, D., Claeskens, G., Wand, M. (2005). Exact likelihood ratio test for penalized splines. Biometrika92 91–103.
Dalgaard, P. (2002). Introductory Statistics with R. Springer, New York.
de Boor (1978). A Practical Guide to Splines. Springer, Berlin.
Efron, B. (2001). Selection criteria for scatterplot smoothers. The Annals of Statistics29 470–504.
Eilers, P., Marx, B. (1996). Flexible smoothing with B-splines and penalties. Statistical Science11 89–121.
Eubank, R. L. (1988). Spline Smoothing and Nonparametric Regression. Dekker, New York.
Fahrmeir, L., Tutz, G. (2001). Multivariate Statistical Modelling Based on Generalized Linear Models. 2nd ed., Springer, New York.
Fan, J., Gijbels, I. (1996). Local Polynomial Modelling and its Applications. Chapman and Hall, London.
Fan, J., Yao, O. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York.
Flaschel, P., Kauermann, G., Semmler, W. (2005). Testing wage and price Phillips curves for the United States. Metroeconomica (to appear).
Grambsch, P.M., Therneau, T. M. (2000). Modelling Survival Data: Extending the Cox Model. Springer, New York.
Green, D. J., Silverman, B.W. (1994). Nonparametric Regression and Generalized Linear Models. Chapman and Hall, London.
Gu, C, Wahba, G. (1991). Smoothing spline ANOVA with component-wise Bayesi-an confidence intervals. Journal of Computational and Graphical Statistics2 97–117.
Härdle, W., Hall, W., Marron, J. S. ((). 1. 98 8.). How far are automatically chosen regression smoothing parameter selectors from their optimum? Journal of the American Statistical Association 83 86–101
Härdle, W., Hall, W., Marron, J. S. (1992). Regression smoothing parameters that are not far from their optimum. Journal of the American Statistical Association87 227–233.
Härdle, W., Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics21 1926–1947.
Härdle, W., Lütkepohl, H., Chen, R. (1997). A review of nonparametric time series analysis. International Statistical Review65 49–72.
Härdle, W., Hlavka, Z., Klinke, S. (2000). XploRe, Application Guide. Springer, Berlin.
Härdle, W., Müller, M., Sperlich, S., Werwatz, A. (2004). Nonparametric and Semiparametric Models. Springer, Berlin.
Hastie, T. (1996). Pseudosplines. Journal of the Royal Statistical Society, Series B58 379–396.
Hastie, T., Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London.
Hastie, T., Tibshirani, R. (1993). Varying-coefficient models. Journal of the Royal Statistical Society, Series B55 757–796.
Hurvich, C.M., Simonoff, J.S., Tsai, C. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Series B60 271–293.
Kauermann, G. (2000). Modelling longitudinal data with ordinal response by varying coefficients. Biometrics56 692–698.
Kauermann, G. (2004). A note on smoothing parameter selection for penalized spline smoothing. Journal of Statistical Planing and Inference127 53–69.
Kauermann, G. (2005). Penalized spline fitting in multivariable survival models with varying coefficients. Computational Statistics and Data Analysis49 169–186.
Kauermann, G., Tutz, G. (2000). Local likelihood estimation in varying-coefficient models including additive bias correction. Journal of Nonparametric Statistics12 343–371.
Kauermann, G., Tutz, G. (2001). Testing generalized linear and semiparametric models against smooth alternatives. Journal of the Royal Statistical Society, Series B63 147–166.
Kauermann, G., Tutz, G., Brüderl, J. (2005). The survival of newly founded firms: A case study into varying-coefficient models. Journal of the Royal Statistical Society, Series A168 145–158.
Loader, C. (1999). Local Regression and Likelihood. Springer, Berlin.
Marron, J.S., Chaudhuri, P. (1999). SiZer for exploration of structures in curves. Journal of the American Statistical Association94 807–823.
McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models. 2nd ed., Chapman and Hall, New York.
Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Application9 141–142.
Nychka, D. (2000). Spatial process estimates as smoothers. In Smoothing and Regression. Approaches, Computation and Application (Schimek, ed.), Wiley, New York.
O’Sullivan, F. (1986). A statistical perspective on ill-posed inverse problems. Statistical Science1 502–518.
Opsomer, J.D., Wang, Y., Yang, Y. (2001). Nonparametric regression with correlated errors. Statistical Science16 134–153.
Pagan, R., Ullah, A. (1999). Nonparametric Econometrics. Cambridge University Press, Cambridge.
Phillips, A. W. (1958). The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861–1957. Economica25 283–299.
Reinsch, C. H. (1967). Smoothing by spline functions. Numerical Mathematics10 177–183.
Rice, J. A. (1984). Bandwidth choice for nonparametric regression. Annals of Statistics12 1215–1230.
Ripley, B.D., Venables, W. N. (2002). Modern Applied Statistics with S. 4th ed., Springer, New York.
Ruppert, D. (2004). Statistics and Finance. Springer, New York.
Ruppert, R., Wand, M. P., Carroll, R. J. (2003). Semiparametric Regression. Cambridge University Press, Cambridge.
Simonoff, J. S. (1996). Smoothing Methods in Statistics. Springer, New York.
Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B36 111–147.
Wand, M. P. (2003). Smoothing and mixed models. Computational Statistics18 223–249.
Wahba, G. (1990). Regularization and cross validation methods for nonlinear implicit, ill-posed inverse problems. In Geophysical Data Inversion Methods and Applications (A. Vogel, C. Ofoegbu, R. Gorenflo and B. Ursin, eds.), 3–13. Vieweg, Wiesbaden-Braunschweig.
Watson, G. S. (1964). Smooth regression analysis. Sankhyā, Series A26 359–372.
Wood, S. N. (2003). Thin plate regression splines. Journal of the Royal Statistical Society, Series B65 95–114.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Berlin · Heidelberg
About this chapter
Cite this chapter
Kauermann, G. (2006). Nonparametric Models and Their Estimation. In: Hübler, O., Frohn, J. (eds) Modern Econometric Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32693-6_10
Download citation
DOI: https://doi.org/10.1007/3-540-32693-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32692-2
Online ISBN: 978-3-540-32693-9
eBook Packages: Business and EconomicsEconomics and Finance (R0)