Asymptotics of Fisher information under weak perturbation

An asymptotic expression is derived for the Fisher information of the sum of two independent random variables X and Z/sub /spl epsiv// when Z/sub /spl epsiv// is small, under some regularity conditions on the density of X and conditions on the moments of Z/sub /spl epsiv//. Using this result for the case Z/sub /spl epsiv//=/spl epsiv/Z, some asymptotic generalization of De Bruijn's identity is obtained.