Improving the efficiency of the Harrell-Davis quantile estimator for special cases using custom winsorizing and trimming strategies

Let’s say we want to estimate the median based on a small sample (3 \(\leq n \leq 7\)) from a right-skewed heavy-tailed distribution with high statistical efficiency. The traditional median estimator is the most robust estimator, but it’s not the most efficient one. Typically, the Harrell-Davis quantile estimator provides better efficiency, but it’s not robust (its breakdown point is zero), so it may have worse efficiency in the given case. The winsorized and trimmed modifications of the Harrell...

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