maxpro.remove: Sequentially remove design points from a design while maintaining low maximum projection criterion as possible
Description
This function sequentially removes design points one-at-a-time from a design while maintaining low maximum projection criterion as possible.
Usage
maxpro.remove(D, n.remove, delta = 0)
Value
the updated design.
Arguments
D
design
n.remove
number of design points to remove
delta
a small value added to the denominator of the maximum projection criterion. By default it is set as zero.
Details
maxpro.remove sequentially removes design points from a design while maintaining low maximum projection criterion (see maxpro.crit) as possible. The maximum projection criterion is modified to include a small delta term: $$\phi_{\text{maxpro}}(\bm{D}_n) = \left\{\frac{1}{{n\choose 2}}\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}\frac{1}{\prod_{l=1}^p(x_{il}-x_{jl})^2 +\delta}\right\}^{1/p}.$$ The index of the point to remove is \(k^* =\arg\min_k \sum_{i \neq k}\frac{1}{\prod_{l=1}^p(x_{il}-x_{kl})^2 +\delta}\).