Hi,
I am trying to compare my data with empirical distributions. But I don't have enough data to cut them to estimation data and validation data. I've been looking at bootstrapping, and I understood that this method helps in resampling data and using them to estimate parameters. Can I use this tool to do this :
1. resample the data
2. estimate the parameters of the empirical distribution using a part of the data
3. use goodness of fit test to compare the remaining data with the model with the estimated parameters
Is this a correct way to do this a more general estimation and see if some data follow some empirical distribution ?
If not, is there another way to do this?
At first I was doing parameter estimation on the data and after that doing a goodness of fit test on the data and the model, but this only help in giving a hard no on some models.
Take a look at Efron's presentation of the bootstrap and summaries of its utility. A book: urn:uuid:1a7968f2-a5b9-4103-8889-8f1aaf57f0b4-geonode:GH_Departamentos4326
The standard way to test whether data fits a particular distribution is to do a probability plot.
Here is an example on how to test whether data is normally distributed
http://stats.stackexchange.com/questions/72418/how-to-check-for-normal-distribution-using-excel-for-performing-a-t-test
You will have to something similar for your chosen distribution that you are trying to fit data to.
By bootstrapping, it will not increase the dataset rather it resample them with same number that provides a robust estimation. For the goodness of fit, better if you can do the probability plot/chi-square test/residual analysis.
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