
Accession Number : AD0723837
Title : Optimal and Admissible Designs for Polynomial Monospline Regression,
Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
Personal Author(s) : Bruvold,Norman T.
Report Date : 14 MAY 1971
Pagination or Media Count : 124
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 (nj) where n1= 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 semidefinite 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)
Descriptors : (*EXPERIMENTAL DESIGN, *REGRESSION ANALYSIS), MEASURE THEORY, NUMERICAL ANALYSIS, APPROXIMATION(MATHEMATICS), POLYNOMIALS, OPTIMIZATION, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE