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I'm working on a class project which involves calculating total sales for a given clothing brand from a sample retailer panel. I have monthly sales totals, and I want to estimate quarterly sales for the entire US. I can assume my panel is representative of the total retailer population, however there are occasional spurious data points for particular months/retailers that appear to arise due to data input errors.

My initial thought was to use a leave one out method to identify these outlier facilities. I'm finding the historical percent contribution of each retailer to the total sales, and using this to re-normalize my sample each time I remove a retailer using this method. The retailer I remove at each step is based on the MAD method mentioned here, with the farthest outlying facility removed.

My thought was that as I remove the farthest outlying retailer at each step, the re-normalized panel sales would converge to a steady state value, and then I could scale up to estimate the total US sales based off of my capture rate. The problem is that my estimate seems to jump around with each retailer I remove and never seems to converge.

I'm wondering if there is an error in the way I'm doing the re-normalization, or if this is just a fundamentally flawed methodology. This intuitively seems like it should work, but is there a better way to approach this problem?

Thanks in advance for any advice!

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