Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Statistics and Probability

2005

Optimization

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Spatial Sampling Design For Parameter Estimation Of The Covariance Function, Zhengyuan Zhu, Michael L. Stein Sep 2005

Spatial Sampling Design For Parameter Estimation Of The Covariance Function, Zhengyuan Zhu, Michael L. Stein

Zhengyuan Zhu

We study the spatial optimal sampling design for covariance parameter estimation. The spatial process is modeled as a Gaussian random field and maximum likelihood (ML) is used to estimate the covariance parameters. We use the log determinant of the inverse Fisher information matrix as the design criterion and run simulations to investigate the relationship between the inverse Fisher information matrix and the covariance matrix of the ML estimates. A simulated annealing algorithm is developed to search for an optimal design among all possible designs on a fine grid. Since the design criterion depends on the unknown parameters, we define relative …

Go to article

On Optimizing Multi-Level Designs: Power Under Budget Constraints, Todd C. Headrick, Bruno D. Zumbo Jan 2005

On Optimizing Multi-Level Designs: Power Under Budget Constraints, Todd C. Headrick, Bruno D. Zumbo

Todd Christopher Headrick

This paper derives a procedure for efficiently allocating the number of units in multi-level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A …

Go to article