Advertisement

Curve-Fitting

  • Ezra Hauer
Chapter

Abstract

Curve-fitting1 is based on the belief that hidden under the data cloud there is an orderly relationship between the E{μ} and the population-defining traits. The key feature of curve-fitting is that use is made of data from neighboring populations to fashion estimates for specific populations. This is intended to alleviate the “sparse data problem.” But curve-fitting is not an unmixed blessing. As it irons out unwanted randomness, it distorts some of what is real. When curve-fitting is “nonparametric,” one only has to specify a rule by which an estimate is to be computed from neighboring data. For “parametric” curve-fitting, the modeler has to assume that the underlying orderly relationship can be represented by some equation, and then to estimate its parameters. To illustrate the nature of nonparametric curve-fitting, the “Nadaraya-Watson Kernel Regression” will be applied to the Colorado data.

Keywords

Model Equation Smooth Curve Segment Length Bell Curve Neighboring Data 
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.

References

  1. AASHTO (The American Association of State Highway and Transportation Officials) (2010) Highway Safety Manual, 1st editionGoogle Scholar
  2. Elvik R (2011) Assessing causality in multivariate accident models. Accident Anal Prev 43:253–264CrossRefGoogle Scholar
  3. Hauer E (2010) Cause, effect, and regression in road safety: a case study. Accident Anal Prev 42:1128–1135CrossRefGoogle Scholar
  4. Li Q, Racine JS (2007) Nonparametric econometrics: theory and practice. Princeton University, PrincetonzbMATHGoogle Scholar
  5. Lord D, Bonneson JA (2007) Development of accident modification factors for rural frontage road segments in Texas. Transport Res Rec 2023:20–27CrossRefGoogle Scholar
  6. Nadaraya EA (1964) On estimating regression. Theor Probab Appl 9(1):141–142CrossRefzbMATHGoogle Scholar
  7. Simonoff JS (1996) Smoothing methods in statistics. Springer, New YorkCrossRefzbMATHGoogle Scholar
  8. Watson GS (1964) Smooth regression analysis. Sankhya Ser A 26:359–372MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ezra Hauer
    • 1
  1. 1.University of TorontoTorontoCanada

Personalised recommendations