\(L^1\) bounds in normal approximation (Q2456032)

The author derives normal approximation bounds for the \(L^1\) distance between distribution functions in a variety of examples: the case of sums of independent random variables, projections of cone measure on the sphere, simple random sampling and combinatorial limit theorems. As a tool, he uses a basic coupling inequality, which says that the \(L^1\) distance between a standardized distribution function \(F\) and a standard normal one is bounded by two times the expectation of the absolute value of the difference of a random variable with distribution function \(F\) and its zero biased transformation.