The non uniform bound of the remainder in the central limit theorem for the sums of functions of uniform spacings is established. The bound depend on the moments of functions of the standard exponential random variables.
Mirakhmedov, S. and Kalandarov, U. (1998) "The Non Uniform Bounds of Remainder Term in CLT for the Sum of Functions of Uniform Spacings," Turkish Journal of Mathematics: Vol. 22: No. 1, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol22/iss1/5