Direct comparison of stealing doubts
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1. The Optimization criterion Is the Same
1.1 He(2009)'s Optimization criterion
1.1 He(2009)'s Optimization criterion
Figure 1.1 He(2009)'s Optimization criterion mcc
1.2 Optimization criterion in Lin(2009)
1.2 Optimization criterion in Lin(2009)
In Lin(2009)[Biometrika, Volume 96, Issue 1, March 2009, Pages 243–247], C.D.Lin defined an Optimization criterion max, see Fig. 1. 2,
Figure 1.2 Lin(2009)’s Optimization criterion max
1.3 Optimization criterion in Lin(2008,2010) & Bingham(2009)
1.3 Optimization criterion in Lin(2008,2010) & Bingham(2009)
The optimization criterion in Lin (2008, 2010) and Bingham (2009) are shown in Figure 1.3,
Figure 1.3 optimization criterion in Lin (2008, 2010) and Bingham (2009)
2. The Necessary Condition of the Existence Theorem Is the Same
2. The Necessary Condition of the Existence Theorem Is the Same
2.1 He(2009)'s Existence Theorem for the zero correlation designs
2.1 He(2009)'s Existence Theorem for the zero correlation designs
In English： A necessary condition for the existence of the zero correlation arrays is that m is either an odd number greater than 3, or a multiple of 4. The zero correlation arrays don't exist if the run size of the design is 4k+2, where k is a positive integer.
2.2 Lin(2008)'s Existence Theorem for the orthogonal Latin hypercube designs
3 Exchange Algorithm Is the Same
3 Exchange Algorithm Is the Same
3.1 He(2009)'s an Exchange Algorithm
3.1 He(2009)'s an Exchange Algorithm
In english: Supposing the two subscripts are i and j, whose corresponding to two components to be exchanged of x respectively, and assuming i < j ( if i > j, the discussion method and result are the same), and Letting x' denote a new vector obtained after exchanging. The relationship between both inner products of old and new is that formula (2.4).
In english: Supposing the two subscripts are i and j, whose corresponding to two components to be exchanged of x respectively, and assuming i < j ( if i > j, the discussion method and result are the same), and Letting x' denote a new vector obtained after exchanging. The relationship between both inner products of old and new is that formula (2.4).
3.2 Lin(2008)'s an Exchange Algorithm
3.2 Lin(2008)'s an Exchange Algorithm
4 The Stacking Operation for the Designs and the Stacking Principle for the Orthogonal Designs Are the Same
4.1 A stacking algorithm and its proof of He (2009)
4.1 A stacking algorithm and its proof of He (2009)
In English :
Two zero-correlation matrices with the same dimension and domain are stacked on top of each other and the result is still a zero-correlation matrix.
Letting A = (a1, . . . , ap), and B = (b1, . . . , bp) be two m×p zero correlation matrices, stack them form a 2m × p matrix C = (c1, . . . , cp). It is easy to verify for (3.1)
4.2 The stacking principle in Lin(2008)p.40 (Lin(2010)p.8)
5. The Both Results are the Same
5. The Both Results are the Same
5.1 An example of He(2009)
5.1 An example of He(2009)
Figure 5.1 An example of He(2009)
5.2 An example in Lin (2009) and report correlation parameters in my way
Figure 5.2 An example in Lin (2009) and report correlation parameters in my way
5.3 An Example of Weak Correlation with 16 Runs
5.3 An Example of Weak Correlation with 16 Runs
Figure 5.3 W16f5o from He (Construction date: June 10,2006)
Figure 5.4 An example in Lin(2008)p.27 and Lin(2010)p.14,
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