# Comparing upper percentile across time

Is there a test to compare a variable across time When using a cutoff value to select for observations with a particularly high or low value.

I can think of many simple examples for this:

• Did the richest persons (99th percentile) get richer between 2000 and 2010?
• Do persons with a blood pressure above 140mmHg show an increase in blood pressure when watching their favourite football team?
• Did the fastest runners get faster in the Olympics 2004 in comparison to 2000?

My own naive guess is something like a regression to the mean (I hope I am using the term correctly): If the times for running in the Olympics are just randomly correlated across years, then I would expect that those who were fast in 2000 are likely to be slower in 2004.
The other case when the rich become richer from year to year holds rather true for money.

• thickest looks like a typo for richest. (In some versions of English, thickest is informal for most stupid and so pejorative, if not offensive, unless used with modest self-reference.) – Nick Cox May 14 '18 at 12:47
• These are just special cases of quantile regression which is the key term you seek. As the predictor is time, worry about dependence of errors might be appropriate. – Nick Cox May 14 '18 at 12:48
• Thanks a lot for your comments so far. Although I was refering to the waist size, I chose a more suitable example. – NicolasBourbaki May 14 '18 at 13:03
• That would be fattest except that circumlocution about circumference using a term like waist size would often be preferred. – Nick Cox May 14 '18 at 13:17
• "a blood pressure above 140 mmHg" would usually mean different percentiles in different years. – Nick Cox May 14 '18 at 13:44