On a central limit theorem for shrunken weakly dependent random   variables
  A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For independent, identically distributed random variables, this result was proved earlier by Housworth and Shao. 
Richard C. Bradley and Zbigniew J. Jurek
math.PR