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I have points in the x-y-plane that are strictly increasing most of the time. The problem is that there are cases with one or two outliers (Knots where an out-of-the-box spline would be decreasing). Without deleting any data points, is there a way to interpolate / create a spline that is strictly increasing everywhere? Also, I would like the interpolation to be $C^1$. (Which package could do this in R?)

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    $\begingroup$ What is $C^1$? Other than that, it sounds like isotonic regression might be a good fit for you needs. $\endgroup$ – Sycorax Oct 29 '15 at 20:49
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    $\begingroup$ mgcv can fit general penalised regression models with monotonicity constraints using cubic splines. mgcv has function mono.con for constraints on a cubic spline, and the models are fitted using the pcls() function - the help page of which has an example. $\endgroup$ – Gavin Simpson Oct 29 '15 at 21:02
  • $\begingroup$ @user777 $C^1$ denotes the smoothness; maybe it is not internationally used - i studied math in Germany. (cf. en.wikipedia.org/wiki/Smoothness) $\endgroup$ – dotwin Oct 31 '15 at 2:23
  • $\begingroup$ @both: upvotes + thx a bunch for your suggestions; I will look into it now. $\endgroup$ – dotwin Oct 31 '15 at 2:24
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    $\begingroup$ CV user Rob Hyndman has some functions available: robjhyndman.com/software/monotonic-splines $\endgroup$ – mark999 Oct 31 '15 at 3:27
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R package cobs allows you to fit shape-constrained splines, including monotonically increasing ones; syntax would be something like:

require(cobs)
fit = cobs(x,y,
      constraint= "increase", 
       lambda=0, 
       degree=1, # for L1 roughness
       knots=seq(min(x),max(x),length.out=10), # desired nr of knots 
       tau=0.5) # to predict median
preds = predict(fit,interval="none",z=xvals)[,2]

And R packages ConSpline, scar, scam and cgam offer also alternative options to fit shape-constrained splines, including monotonically increasing ones....

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