Hi I have a set of 10 data sets sampled over 10 years. For each year i estimate a statistic from the data.
example
x = 0,1,2,3,4,5,6,7,8,9,10
y= 0.5,0.86,3,4,6,8.7,9.3,9.9,11 <-estimated statistic from my data
For each estimated value I have a bootstrap distribution.
I then fit several linear and nonlinear models to this data using least squares (e.g linear,polynomial,exponential,logistic).
I am not thinking of using the chi square goodness of fit formula to find the best fit
where is the degrees of freedom and is the variance from my bootstraps.
The model with closest to 1 is the model which best fits the data.
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Does this methodology sound valid. I think the chi square test assumes my error distribution/bootstraps are normal. Can anyone recommend something better? or any criticisms
Sorry Ill give some more information and my goal
So as I described I have these 10 data sets sampled at times . Specifically each data set is genetic data from influenza patients at time .
For each data set I calculate a statistic which summarizes the data. This statistic is just a simple counting method. Lets call the results from this statistic
so now I am in a position to do some regression analysis on data
Ok now because i wanted to know the distribution of my statistic I used a bootstrapping approach. Therefore for each time point I have a vector with the bootstrap distribution .
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My Question/Goal - I want to fit a series of models to my data and then test which of these models best fits my data. i.e lets say an exponential model best fits my data.
I though of using the chi square goodness of fit test for each model, but also i could use leave one out cross validation.
Is this enough information? Thanks for your time, I hope this is slightly more clear