Fisher information and the central limit theorem
  An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions. 
S. G. Bobkov, G. P. Chistyakov and F. G\"otze
math.PR math.ST stat.TH