Graduate Bivariate Smoothing Splines

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A request for a bivariate smoothing spline package that allows customization of the loss function is presented, specifically seeking alternatives to public domain software like SCIPY, which typically minimizes the sum of squared errors. The user expresses a desire to maximize the log-likelihood of a Cauchy distribution for the errors instead. While acknowledging the possibility of using a black box optimizer to set up the problem independently, the discussion hints at challenges related to the number of knots in the spline. The need for more flexible spline options in statistical modeling is emphasized. Overall, the conversation highlights a gap in available tools for specific statistical needs.
Joe Prendergast
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Does anyone know of a bivariate smoothing spline package that lets you set your own loss function? All of the public domain software I've been able to find (e.g., SCIPY) appears to minimize the sum of squared errors. For example, I'd like to set the spline coefficients to maximize the log-likelihood of a Cauchy distribution of the errors.
 
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You could just use a black box optimizer and set the problem up yourself. Depending on how many knots you have...
 
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