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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.

    tumblr_inline_mkjio64Ow01qz4rgp.jpg

    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
    or
    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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