Closeness estimate for probability distribution and its zero bias transform / I. S. Tyurin. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 4. P. 55-58 [Moscow Univ. Math. Bulletin. Vol. 67, N 4, 2012.].
We propose a new concise and transparent proof for the optimal estimate concerning the mean metric distance between a probability distribution and its zero bias transformation.
Key words: normal approximation, Stein's method, zero biasing.