Central limit theorems for four new types of U-designs

Xiangshun Kong, Mingyao Ai*, Rahul Mukerjee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Orthogonal array (OA)-based Latin hypercube designs, also called U-designs, have been popularly adopted in designing a computer experiment. Nested U-designs, sliced U-designs, strong OA-based U-designs and correlation controlled U-designs are four types of extensions of U-designs for different applications in computer experiments. Their elaborate multi-layer structure or multi-dimensional uniformity, which makes them desirable for different applications, brings difficulty in analysing the related statistical properties. In this paper, we derive central limit theorems for these four types of designs by introducing a newly constructed discrete function. It is shown that the means of the four samples generated from these four types of designs asymptotically follow the same normal distribution. These results are useful in assessing the confidence intervals of the gross mean. Two examples are presented to illustrate the closeness of the simulated density plots to the corresponding normal distributions.

Original languageEnglish
Pages (from-to)655-667
Number of pages13
JournalStatistics
Volume51
Issue number3
DOIs
Publication statusPublished - 4 May 2017
Externally publishedYes

Keywords

  • Central limit theorem
  • correlation controlled U-design
  • nested U-design
  • sliced U-design
  • strong orthogonal array-based U-design

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