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