What is the intuition behind the generalized confidence interval?

Question

What is the intuition behind the generalized confidence interval? My best description on GCI that it is the way to derive a formula to calcuate the area of the center region in a asymetry distribution where it has the two-sided-equal-tailed regions in which the area of the two-sided-equal-tailed regions are the same in the n dimensional case. A paper on the GCI: http://www.stat.colostate.edu/statresearch/stattechreports/Technical%20Reports/2002/02_10.pdf Also: http://www3.stat.sinica.edu.tw/statistica/oldpdf/a10n420.pdf

Answer 1

Hello!

Confidence intervals give you information about the range of possible values that are likely to contain the TRUE value (called the population parameter) of what you are trying to estimate. For example, if you want to know how much cheese your cat eats each day, one way to figure this out is to follow your cat carefully for 5 days and record the average daily amount of cheese your cat ate over these 5 days. Although this average amount over 5 days is helpful, it may not tell us the whole story. For example, perhaps one of the humans in your family had a birthday during these 5 days and there was plenty of leftover cake from the party. If the extra cake was fed to the cat, then the cat probably ate less cheese than he normally would. Thus, we would also like to have an idea about how different the true value of cheese your cat generally eats might be from the amount of cheese your cat ate over those 5 days, and this is what the confidence interval tells us.

I hope this helps with the intuition, and please let me know if you have any follow-up questions. Also, Khan Academy has some really helpful videos that cover this topic in their Probability course found here:

https://www.youtube.com/watch?v=uhxtUt_-GyM&list=PL1328115D3D8A2566