Improvements on removing non-optimal support points in D-optimum design algorithms

Details Improvements on removing non-optimal support points in D-optimum design algorithms Improvements on removing non-optimal support points in D-optimum design algorithms

2007-06-29

arxiv.org/abs/0706.4394v1

Statistics & Probability Letters / Statistics and probability Letters 77 (2007) 90-94

Mathematics

Statistics Theory

5 pages Statistics and Probability letters available online at: http://www.elsevier.com/locate/stapro

Scientific paper

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let $\xi$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+\epsilon$ be the maximum of the variance function $d(\xi,\mathbf{x})$ over all $\mathbf{x} \in \mathcal{X}$. We prove that any support point $\mathbf{x}_{*}$ of a $D$-optimum design on $\mathcal{X}$ must satisfy the inequality $d(\xi,\mathbf{x}_{*}) \geq m(1+\epsilon/2-\sqrt{\epsilon(4+\epsilon-4/m)}/2)$. We show that this new lower bound on $d(\xi,\mathbf{x}_{*})$ is, in a sense, the best possible, and how it can be used to accelerate algorithms for $D$-optimum design.

Affiliated with

Also associated with

No associations

Rating

Improvements on removing non-optimal support points in D-optimum design algorithms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Improvements on removing non-optimal support points in D-optimum design algorithms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Improvements on removing non-optimal support points in D-optimum design algorithms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-681789