Large "O" and small "o" approximations of the expected value of a class of smooth functions (f [set membership, variant] Cr(R)) of the normalized partial sums of dependent random variable by the expectation of the corresponding functions of normal random variables have been established. The same...

A uniform estimate of the rate of convergence in the central limit theorem (CLT) in certain Banach spaces for dependent random variables is established when the Gaussian measure of the [epsilon]-neighbourhood of the boundary of a set is proportional to [epsilon] and the third order moment is...