Minimally Supported D-optimal Designs for Response Surface Models with Spatially Correlated Errors
碩士 === 國立中山大學 === 應用數學系研究所 === 100 === In this work minimally supported D-optimal designs for response surface models with spatially correlated errors are studied. The spatially correlated errors describe the correlation between two measurements depending on their distance d through the covariance...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2012
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/00308011139181529380 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 100 === In this work minimally supported D-optimal designs for response surface models with spatially
correlated errors are studied. The spatially correlated errors describe the correlation between two
measurements depending on their distance d through the covariance function C(d)=exp(-rd). In one
dimensional design
space, the minimally supported D-optimal designs for polynomial models with spatially correlated errors
include two end points and are symmetric to the center of the design region. Exact solutions for simple
linear and quadratic regression models are presented. For models with third or higher order, numerical
solutions are given. While in two dimensional design space, the minimally supported D-optimal designs
are invariant under translation、rotation and reflection. Numerical results show that a regular triangle
on the experimental region of a circle is a minimally supported D-optimal design for the first-order
response surface model.
|
|---|