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Homework Help: Searching for appropriate statistical model

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant 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
    Y <= a1*x1 + a2*x2 + ... + an+xn + e

    3. 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!
  2. jcsd
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