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Independence assumption methods assume ρ = 0, implying that the variance equals 1.
However, the independence assumption is often violated in practice.
So, that was a failure of the independence assumption in finance.
A special attention is paid to the role and applicability of "local independence" assumption.
In order to compute the quantile function, we may use either an independence assumption or a Markov assumption.
On the other hand, the conditional independence assumption becomes less severe when inter-observation times are relatively short.
2. The sample was randomly selected (independence assumption).
We first extend ICA methods and relax the independence assumption.
Another important assumption is the Conditional Independence Assumption (CIA).
Statistical matching methods rely critically on the conditional independence assumption.
However, under the independence assumption, we can show the equivalence.
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