Does bootstrap require IID?

Does bootstrap require IID?

The Bootstrap (Efron 1979) assumes that the data are IID. Obviously, if we have time series data then we probably cannot make that assumption unless we have a special case that we a time series of IID noise.

Why is the IID assumption needed?

The i.i.d. assumption is important in the classical form of the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. Often the i.i.d. assumption arises in the context of sequences of random variables.

What are the assumptions in the bootstrap method?

Additional assumptions, such as linearity, smoothness, symmetry, homoscedasticity, and bias, depend upon the statistic, and your method of bootstrapping it. Bootstrapping does not assume your sample is the same as its population – unless you have sampled the entire population this is clearly impossible.

Are there any problems with using bootstrap confidence intervals?

Aside from the bootstrap statistic having to use the same formula as the (population) statistic being estimated, bootstrap confidence limits suffer many of the same problems as ordinary confidence intervals. Although there are problems if a statistic is distributed asymmetrically, heteroscedacticity is more difficult to allow for.

What is the purpose of second stage bootstrap?

Second-stage bootstrapping, which resamples each bootstrap sample, aims to estimate the errors of the first-stage estimates. Some forms of bootstrapping modify the model population’s parameters to meet specific hypotheses – assuming, of course, both the modification and its effects are plausible.

When to bootstrap or resample data with replacement?

There are many ways of going about this process, and modifications thereof, but they share a common underlying logic. Bootstrapping, or resampling data with replacement, is justified to the extent it replicates how that data were obtained – at any rate, if this assumption is unrealistic, its results should be treated accordingly.