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I have some data that I'd like to create an envelope for it.

enter image description here

As in the picture, the data is always positive and I'm looking for something that will capture my crudely hand drawn red line. It should be eventually possible to predict from the fit model actual points on the line. The shape of the envelope does not necessarily follow any general function. I'm maybe looking for a LOESS-type fit, just for maximum values.

The data itself are the squared residuals from a fit, and I am looking to predict the variance at various x values.

Gimelist
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    There is no unique solution. For instance, the geometric "alpha hull" algorithm has a tunable parameter that adjusts the "stiffness" of the hull, providing infinitely many solutions. Thus, to make any meaningful progress, you need to consider (1) the nature of the data--especially any uncertainty in their values--and (2) the intended interpretation or use of the hull. Could you share this kind of information in an edit to your question? – whuber Mar 27 '15 at 01:12
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    Your hand drawn curve is biased. At x=40 and x=60, there should be a dip in the curve. You can divide your data into bins of x and get maximum y values for each of those bins and then apply loess curve there. It will be helpful if you post your data here. – rnso Mar 27 '15 at 01:23
  • You'd need to add some information (conditions, assumptions) to make your problem well-formulated. – Glen_b Mar 27 '15 at 01:25
  • @rnso - as I said, it's crudely drawn. – Gimelist Mar 27 '15 at 02:24
  • @Glen_b this is completely empirical data, and there are few assumptions if any at all. This shouldn't follow any specific distribution. – Gimelist Mar 27 '15 at 02:25
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    I'm talking about assumptions about the way the curve should work. As it stands your problem would allow almost anything above all points as an answer. – Glen_b Mar 27 '15 at 02:28
  • @Glen_b yea, I know. It's not well defined. Maybe something that has some smoothing argument (similar to loess span) that I can play with until it looks ok? – Gimelist Mar 27 '15 at 06:16

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