Abstract

Let f be an integrable function from R3 to R and μ = )[0,1]3 f (x)dx. A simple estimator of μ is ˆμ =
1
n
n *i=1
f ? Xi where
X1, X2, ...Xn are independent random vectors and uniformly distributed on [0, 1]3. In 2006, Neammanee and Laipaporn
used the orthogonal array to choose the points Xi’s and established a non-uniform concentration inequality. In this article,
we improve their result.

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