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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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Optimal hypothesis testing for sum of random variables
If $\frac{p_0(x)}{p_1(x)}$ is a non-decreasing function of $x$, how can I prove that $\frac{p_0(x)^{*n}}{p_1(x)^{*n}}$ is a non-decreasing function of $x$, where
$f^{{*n}}(x)=\overbrace {f(x)*f(x …
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Hypothesis testing to discriminate between two renewal processes
We have time [0,T] to observe a renewal point process, where the inter-renewal timings are i.i.d, and then decide whether the observation is according to a renewal process in which the pdf of inter-r …
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Likelihood ratio testing on infinite dimensional vector
I am performing a likelihood ratio test on a vector containing observations $\textbf{a}$. The number of observation is a random variable $\in \{1,2,\ldots\}$, so the vector of observations may have …