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A central limit theorem is proved for some strictly stationary sequences ofrandom variables that satisfy certain mixing conditions and are subjected tothe "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. Forindependent, identically distributed random variables, this result was provedearlier by Housworth and Shao.

On a central limit theorem for shrunken weakly dependent random variables