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In this paper, the concept of generalized variable resolution is proposed for designs with nonnegligible interactions between groups. The conditions for the existence of generalized variable resolution designs are discussed. Connections between different generalized variable resolution designs and compromise plans, clear compromise plans and designs containing partially clear two-factor interactions...
Latin hypercube designs have found wide application in computer experiments. A number of methods have recently been proposed to construct orthogonal Latin hypercube designs. In this paper, we propose an approach for expanding the orthogonal Latin hypercube design in Sun et al. (Biometrika 96:971–974, 2009) to a nearly orthogonal Latin hypercube design of a larger column size. The newly added part...
Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal $$2^{n-m}$$ designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria...
Stein’s method is used to derive an error in normal approximation for sums of pairwise negative quadrant dependent random variables, but under the assumption of second moment only. This allows us to derive a central limit theorem for pairwise negative quadrant dependent random variables with Lindeberg’s condition.
The product of partial sums of linear positive (negative) quadrant dependent, positive random variables is asymptotically lognormal. This extends the earlier work on independent, positive random variables [see Rempala and Wegolowski Elect Comm Probab 7:47–54, 2002].
Let $$\{X_{n}; n\geq 1\}$$ be a sequence of stationary positively associated random variables and a sequence of positive constants $$\{b(n); n\geq1\}$$ be monotonically approaching infinity and be not asymptotically equivalent to loglog n. Under some suitable conditions, a nonclassical law of the iterated logarithm is investigated, i.e. $$\limsup_{n\rightarrow\infty}\frac{\sum_{i=1}^{n}[f(X_{i})-E...
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