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Hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect).
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Comparing two proportions asymptotic distribution
Thanks for pointing out the earlier, crucial (and pretty bad) mistake. Hopefully the following answer is more or less correct...
Suppose, for the moment, that $n_Y = \lceil c n_X \rceil$, for some $c …
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How to derive the asymptotic distribution of the test statistic of a large sample test for e...
The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: Thanks f …
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Fractional Gaussian noise, the KPSS test, and stationarity
Looking at the Kwiatkowski paper, they assume the model
$$ y_t = r_t + \varepsilon_t$$ (forgetting about the trend, i.e. setting $\xi = 0$ in their model).
Here $(r_t)$ is a random walk
$$ r_t = r_{t …