A Uniform Bound on a Combinatorial Central Limit Theorem

Uniform Bound on Normal Approximation of Latin Hypercube Sampling

“…We apply the idea of Neammanee and Rattanawong (Neammanee, K. & Rattanawong, P., 2008) and the fact that…”

“…From now, we use the following system giving by Ho and Chen (Ho, S.T., 1978) and Neammanee and Rattanawong (Neammanee, K. & Rattanawong, P., 2008). …”

“…In the case of d = 2, we observe that this is a special case of the combinatorial central limit theorem (For more detail see Von Bahr (Von Bahr, B., 1976), Ho and Chen (Ho, S.T., 1978)). Under the finiteness of absolute third moment, Neammanee and Suntornchost (Neammanee, K. & Suntornchost, J., 2005) gave the uniform rate of convergence and obtained the rate 198 √ n . Recently, Neammanee and Rerkruthairat (Neammanee, K. & Rerkruthairat, N.) improve the constant to be 78.36.…”

“…In this article, we use a concentation inequality approach of Stein's method with ideas of Neammanee and Rattanawong ( (Neammanee, K. & Rattanawong, P., 2008), (Neammanee, K. & Rattanawong, P., 2009b)) and Neammanee and Rerkruthairat (Neammanee, K. & Rerkruthairat, N.) to obtain a constant C d by assuming the finiteness of the absolute third moment. Theorem 1.5 is our main result.…”

“…Furthermore, Neammanee and Rattanawong (Neammanee, K. & Rattanawong, P., 2008) used a concentration inequality approach of Stein's method and assumed the finiteness of fourth moment to give a constant C d . This is their result.…”