- #1

aardflouf

- 1

- 0

## 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!