Searching for appropriate statistical model

[aardflouf]

Homework Statement

Hello, I'm looking for direction in finding whether any mathematical models exist for a specific type of trend.

I've created a blog for an online class and have started looking at Mars crater data. The graph below appears to have a maximum value for depth as diameter increases. My goal is to apply a statistical model that describes the top edge of the depth vs diameter plot.

Applying linear regression would not be appropriate in this case, since I'm interested in the edge of the data, not its lower values.

Does a model exist for fitting this type of data?

Homework Equations

Y = a1*x1 + a2*x2 + ... + an+xn + e
doesn't seem to apply here.

I'm looking for something like:
maximum(Y) = a1*x1 + a2*x2 + ... + an+xn + e
or
Y <= a1*x1 + a2*x2 + ... + an+xn + e

The Attempt at a Solution

One option is to write a program that picks the top n values for each increment along the x-axis (diameter), but this would not provide reproducible results, and would be too sensitive to outliers.

I've searched for:

• inequality-constrained linear models
• boundary models
• linear threshold model

none of these were insightful. is anyone familiar with models that would be appropriate for this type of data?

Thanks in advance!

 

[Nino MMP]

A possible solution could be to use a non-linear regression model such as polynomial regression or spline regression. These models can capture the shape of the data more accurately than a linear regression model, and can account for the edge of the data as well. You could also try using a smoothing technique such as loess regression.