Steck provides several approximations for the multivariate Mills' ratio. We first prove a new result for the univariate Mills' ratio and use it to give simple sufficient conditions for Steck's best approximation to be a lower bound.
@article{1176992380,
author = {Iyengar, Satish},
title = {On a Lower Bound for the Multivariate Normal Mills' Ratio},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 1399-1403},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992380}
}
Iyengar, Satish. On a Lower Bound for the Multivariate Normal Mills' Ratio. Ann. Probab., Tome 14 (1986) no. 4, pp. 1399-1403. http://gdmltest.u-ga.fr/item/1176992380/