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Tail fitting, quantile interpolation [21]

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Bullet points include: Interpolate over what quantile range? If fit to 100% of observations then akin to MLE, but the wider the range the more we have to assume that we understand the underlying distributional form. See impact of fitting to, say, worst 1%, 3%, 10% or 100% of simulations (using TWMLE, since clearer convergence to MLE as %age tends to 100%). Using: a) Basic Monte Carlo (simulations chosen ‘at random’). b) (Basic) low discrepancy (Halton) sequences. As a) or b) but replacing original draw sequences with their principal components (which are orthogonal by construction) and with the principal components adjusted to match assumed means and standard deviations of factors. Approach c) forces distribution to have overall observed moments and correlations very closely aligned to underlying distribution, so if interpolating over 100% of observations should then get almost exact answer

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