Originally Posted by

**chogo** 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

$\displaystyle \chi^2 = 1/v \sum_{i=1}^{10}\frac{(O_i-E_i)^2}{\sigma_i^2}$ where $\displaystyle v$ is the degrees of freedom and $\displaystyle \sigma$ is the variance from my bootstraps.

The model with $\displaystyle \chi^2$ 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