. Introduction Among others, Feller (1971, page 538) gives a formula for the approximation er- ror of the central limit theorem (CLT … i,j 2). Applying the central limit theorem for vectors to the mutually independent x k yields the following theorem …. Introduction Among others, Feller (1971, page 538) gives a formula for the approximation er- ror of the central limit theorem (CLT …

this kind of theorem in random sampling can be simpli ed by using the central limit theorem for independent, random vectors … approximation formula for the variance emerges as by-product from the central limit theorem without using second order inclusion … prob- abilities. Keywords: Central limit theorem; Error normal approximation; Simple random sampling; Unequal probability …

This paper is a survey of the main results on the central limit theorem (CLT) and its invariance principle (IP) for …

are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions …

central limit theorem for the log determinant of the sample covariance matrix in the high-dimensional setting where the …

differences”. Existing results for this approach are substantially extended by proving a functional central limit theorem for the …

Trotter–Kato approximations of mild solutions of such equations. As an application, a classical limit theorem on the …

Limit Theorem and his Weak Law of Large Numbers are false. …

variances σ12,σ22,…. Then we present a central limit theorem for the randomly weighted averages Sn=R1X1+⋯+RnXn, where the random …