Student Puzzle Corner
Bulletin Editor Anirban DasGupta writes the solution to the previous puzzle.
The exact problem was this:
Fix $\epsilon 0$. Give examples of two absolutely continuous distributions with densities $f$ and $g$ such that $|f(x)-g(x)| \leq \epsilon $ for all $x$, and one of the two distributions is infinitely divisible…
The deadline for the Student Puzzle printed in the last issue is October 20, 2015, so there is still time to enter! The puzzle appears at https://imstat.org/2015/08/student-puzzle-corner-11/. We await your submission!…
Infinite divisibility of Euclidean random variables and vectors has been a core theme in the theory of probability for at least sixty years. The question asked is when can a random variable be decomposed into small independent components. Precisely, a random variable (vector) $X$ is called infinitely divisible if for…
Bulletin Editor Anirban DasGupta writes:
The problem asked was to settle the possibility of consistent estimation with incomplete data in three examples, and to provide a concrete one when consistent estimation is possible.
Intuitively, in case (a), you can only infer about $|\mu |$, but not the sign of $\mu…
In this issue, we look at the consequences of having only incomplete data. For example, suppose a random variable $X$ has a normal distribution with mean $\mu $ and variance $\sigma ^2$, and both parameters need to be estimated. With usual data, which we call complete data, namely iid copies…