Berry–Esseen Bound for a Sample Sum from a Finite Set of Independent Random Variables

On Edgeworth Expansions in Generalized Urn Models

“…Also, a very special case of (2.5) is the most commonly used formula of Erdös and Renyi (1959) for investigating the sample sum in a without-replacement scheme (see e.g. Babu and Singh (1985), Zhao et al (2004) and Hu et al (2007)). Formula (2.3) is also useful in studying large deviation problems (see e.g.…”

Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population

“…the case of sum of independent r.v.s, is excluded. In Zhao et al (2004) and Hu et al (2007a) this limitation was covered by using the approach suggested by von Bahr (1972)…”

“…Proof based on the formula (2.17) of Bahr, hence we use denotes (2.16). Also we shall develop some ideas of Mirakhmedov (1983) , Zhao et al (2004) and Hu et al (2007a…”

“…Von Bahr's bound has been improved in Corollary of Mirakhmedov (1985) and in Theorem 1 of Zhao et al (2004). Two terms Edgeworth asymptotic expansion result has been established by Mirakhmedov (1979) and Hu et al (2007a), whereas expansion with arbitrary number of terms was obtained by Mirakhmedov (1983).…”

The Validity of Instruments Revisited

“…Then under Ω being finite and nonsingular, via Assumption 2, Corollary 1 of Zhao, Wang, Wu (2004) shows that…”