Amber Watkins gave me a suggestion on the animation for the ratio estimation, and I think this is a good topic for my animation package. I’ve finished writing the initial version of the function sample.ratio() for this package, which will appear in the version 1.1-2 a couple of days later.
As we know, the benefit of ratio estimation is that sampling skewness may be adjusted for, because the estimation of \(\bar{Y}\) will make use of the information in the relationship of X and Y: \(\bar{X} \cdot (\bar{y}/\bar{x})\). Here is a demo (we can see the ratio estimate, denoted by the red line, generally performs better than \(\bar{y}\)):
