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Can a bootstrap be used to obtain uncertainty estimates?
I appreciate the usefulness of the bootstrap in obtaining uncertainty estimates, but one thing that’s always bothered me about it is that the distribution corresponding to those estimates is the distribution defined by the sample.
By sampling from the empirical distribution (which is known) we can see the relationship between the bootstrap samples and the empirical distribution (the population for the bootstrap sample). Now we infer that the relationship from bootstrap samples to empirical distribution is the same as from the sample to the unknown population.
Which is the main trick of bootstrapping theory?
The main trick (and sting) of bootstrapping is that it is an asymptotic theory: if you have an infinite sample to start with, the empirical distribution is going to be so close to the actual distribution that the difference is negligible. Unfortunately, bootstrapping is often applied in small sample sizes.
When to use bootstrapping in small sample sizes?
Unfortunately, bootstrapping is often applied in small sample sizes. The common feel is that bootstrapping has shown itself to work in some very non-asymptotic situations, but be careful nonetheless.
How is the bootstrap used in data analysis?
The bootstrap can be used to assess uncertainty of sample estimates. We have previously discussed the importance of estimating uncertainty in our measurements and incorporating it into data analysis 1.
What’s the difference between a bootstrap and a sampling distribution?
The parametric bootstrap generates not only the wrong shape but also an incorrect uncertainty in the VMR. Whereas the true sampling distribution from the bimodal distribution has an s.d. = 1.59, the bootstrap (using negative binomial model) overestimates it as 4.35.
Is the relationship from Bootstrap to empirical distribution the same?
Now we infer that the relationship from bootstrap samples to empirical distribution is the same as from the sample to the unknown population. Of course how well this relationship translates will depend on how representative the sample is of the population.
Which is the best method for uncertainty analysis?
This paper delivers an approach to adding uncertainty analysis to one particular exploratory data analysis method: Weighted Regressions on Time, Discharge, and Season (WRTDS) ( Hirsch et al., 2010 ).
How is a bootstrap method used for water quality?
Block bootstrap approach for water quality trends is developed. Used in conjunction with a flexible statistical model for river water quality. Trends in concentration and trends in flux can be evaluated. Confidence intervals can be estimated for trend magnitude. Based on WRTDS: Weighted Regressions on Time, Discharge, and Season.