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Regression by spline functions

Summery

The article deals with the use of Spline Functions, piecewise polynomial functions, in regression models. According to their use in physics and mathematics where one is interested in fitting smooth curves through given fixed points. Poirier [1973] suggests a method estimating those points. Here it is shown that it is possible to estimate the parameters of a Spline directly from the data by the Least Square Estimator. In part 2, the Spline estimation theory given here is applied to a model originally proposed byBarzel [1972]. Here a cubic, quadratic and linear Spline is used as regression functions.

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References

  1. Ahlberg, J.H., E.W. Nilson, andWalsh: The Theory of Splines and Their Applications. New York 1967.

  2. Barzel, Y.: The Rate of Technical Progress: The ‘Indianapolis 500’; Journal of Economic Theory4, 1972, 72–81.

  3. Hudson, D.J.: Fitting Segmented Curves Whose Join Points have to be Estimated. Journal of the American Statistical Association61, 1966, 1097–129.

  4. Mc Gee, V.E., andW.T. Carleton: Piecewise Regression. Journal of the American Statistical Association65, 1970, 1109–24.

  5. Poirier, D.J.: Piecewise Regression Using Cubic Splines Lectured Oslo 1973 Ec. Soz. Congress.

  6. Powell, M.J.D.: The Local Dependence of Least Squares Cubic Splines. SIAM Journal of Numerical Analysis6, 1969, 398–413.

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Gnad, W. Regression by spline functions. Empirical Economics 2, 69–77 (1977). https://doi.org/10.1007/BF01767473

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Keywords

  • Regression Model
  • Economic Theory
  • Polynomial Function
  • Regression Function
  • Estimation Theory