Optimal and Admissible Designs for Polynomial Monospline Regression,
Abstract
The author considers regression of the form Summation, i= zero to n of ((a sub i)(x sub i)) + Summation, i=1 to h, j= (l sub i) to (k sub i) of ((b sub ij)(x-(xi sub i)) sub +, sup (n-j) where n-1= or > (k sub i) = or > (l sub i) = or > zero, a < (xi sub 1) < . . . < (xi sub h) < b and x(epsilon)(a,b). The author defines admissibility in terms of a positive semi-definite difference of information matrices. Some sufficient conditions for admissibility on the spectrum of a design are given. When l sub 1 = 1, h=1 and xi sub 1 lies in the center of the interval (a,b), optimal experimental designs for the individual regression coefficients are given. Some of the optimal designs are not unique but are convex combinations of two probability measures. Three distinct bases are considered. Extrapolation and minimax extrapolation designs are given for the centered knot situation along with some other special cases. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 14, 1971
- Accession Number
- AD0723837
Entities
People
- Norman T. Bruvold
Organizations
- Purdue University