(Solution) - Many statisticians recommend using trimmed means to estimate a population -(2025 Original AI-Free Solution)

Paper Details

Many statisticians recommend using trimmed means to estimate a population mean yU if there are outliers. The procedure used to find an ?-trimmed mean in an SRS of size n is to remove the largest n? observations and the smallest n? observations, and then calculate the mean of the n(1 ? 2?) observations that remain. Show that the ?-trimmed mean for a finite population U of N observation units is

Where q1 and q2 are the ? and (1??) quantiles, respectively. Now propose an estimator of the population ?-trimmed mean for data from a complex survey using ?F(y) and ?f (y).