I'm having a quite simple question: Why is a spline fit not the best choice everytime? In other words: How do I separate a spline fit from a kernel smoother or a polynomial in a meaningful way? I'm aware of the differences and I can imagine proper applications but imagine a case where you can use each of them. Like, for example, a quadratic curve with "some" noise.

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    $\begingroup$ Generic answer is that every model makes a number of simplified assumptions about the reality and those assumptions fit some problems better then others. $\endgroup$
    – Tim
    Commented Nov 2, 2018 at 9:28
  • $\begingroup$ Thank you! How I would apply this to the example of a quadratic curve? $\endgroup$
    – Ben
    Commented Nov 2, 2018 at 9:40
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    $\begingroup$ You are probably right that splines should be used much more but always is a strong word ... $\endgroup$ Commented Nov 2, 2018 at 9:40
  • $\begingroup$ For some data sets a spline might not interpolate or extrapolate as smoothly as a single simple function, and there are some situations where this might be important. $\endgroup$ Commented Nov 2, 2018 at 15:05
  • $\begingroup$ thank you! But let's say we want to interpolate a guadratic behaviour: Why shall I use spline over kernel or a polynomial? The latter would probably the best but let us add some noise. How to select now? $\endgroup$
    – Ben
    Commented Nov 2, 2018 at 15:25