5.50 harrell_davis_weight

Function File: [X] = harrell_davis_weight (scenarios, observation, alpha)

Compute the Harrell-Davis (1982) quantile estimator and jacknife standard errors of quantiles. The quantile estimator is a weighted linear combination or order statistics in which the order statistics used in traditional nonparametric quantile estimators are given the greatest weight. In small samples the H-D estimator is more efficient than traditional ones, and the two methods are asymptotically equivalent. The H-D estimator is the limit of a bootstrap average as the number of bootstrap resamples becomes infinitely large.
Variables:

• scenarios: number of total scenarios
• observation: input vector for which HD weights shall be calculated
• alpha: quantile (e.g. 0.005)
• X: OUTPUT: HD-weight corresponding to observation vector