Fitting of parameters of function with discrete / integer argument

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Selwyn 2015-6-26

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https://ww2.mathworks.cn/matlabcentral/answers/225457-fitting-of-parameters-of-function-with-discrete-integer-argument

回答： Adam Hug 2015-6-30

Could somebody help me find the proper way to find the parameters for a function with integer arguments? I've conducted a series of measurement:

p_1 , p_2 , p_3 , (p_1+p_2)/2 , (p_2+p_3)/2 , (p_1+p_3)/2, (p_1+p_2+p_3)/3 , ....

(and so on, up to 10 parameters). Each measurement has its own measurement error and I would like to find the proper way to find parameters p_1 , p_2 , p_3, with standard deviation...

Thanks in advance!

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Answer 1

Adam Hug 2015-6-30

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https://ww2.mathworks.cn/matlabcentral/answers/225457-fitting-of-parameters-of-function-with-discrete-integer-argument#answer_184600

Based on your question, I am assuming that you are trying to fit a discrete curve. This is a hard problem in general but you can obtain a reasonable solution by using the "lsqnonlin" function in the Optimization Toolbox. More information can be found here:

http://www.mathworks.com/help/optim/ug/lsqnonlin.html

In the context of least squares, residual is a more sensible metric than standard deviation. You could calculate the R^2 metric for the fit using the residual returned from "lsqnonlin".