Saturday, 8 November 2014

Counterexamples to a Central Limit Theorem and a Weak Law of Large Numbers for capacities

P. Terán (2015). Statistics and Probability Letters 96, 185-189.

This note shows that the main results in a former SPL paper by Chareka are wrong. I approached Chareka with a counterexample to his central limit theorem and he didn't take it very well. He said the example was `pathological' and spoke to me quite dismissively saying that he and I were `not even in the same page'. He sent me an eminently reasonable (negative) referee report from SPL as an example of the wrongness I was incurring in. He somehow was able to overturn the report, I can't see how, and have his paper published. He said that I should accept his results since they had been checked by some of the world's leading experts in measure theory (veridical!!!), at which point I felt so deeply offended by the argument of authority that I just cut all communication.

Some time later I found a counterexample to the other main result in his paper, and said: Well, the world needs to know.

The nice thing about this short note is that is shows that ordinary intuitions about probabilities are misleading when studying the more general framework of capacities.

Up the line: 
·Laws of large numbers without additivity (2014).
·Non-additive probabilities and the laws of large numbers (plenary lecture 2011).

Down the line:

Some related papers have been submitted or are under preparation.

To download, click on the title or here.

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