I have the following process: an item of certain type (there are about 20) has real value. After going though processing (which I don't have any information about) changes its value. It may be smaller or larger, but with two properties: 1. If initially zero then stays zero. 2. Always positive
I need to estimate the change in value based on examples. My example data however is not for item by item. I have sets of items each has various types for which I know the initial value of each item and the total value (summed) of the set that contain the items after processing.
- I know how much of each type I have in each set.
- I don't know how much each type contributes the the total sum of each set.
- I can't test all my data, I have billions of items to work with
- The resulting estimation should be very efficient.
My questions are:
- What method should I use?
- Is this a textbook problem with textbook methods of analysis and solutions?
- How do I determine the sample size?