DESIGN PROBLEMS IN MODEL ROBUST REGRESSION AND EXACT D-OPTIMALITY
Abstract
This thesis deals with two different yet related areas of optimal experimental design. In the first part we seek designs which are optimal in some sense for extrapolation and estimation of the ith derivative at 0 when the true regression function is in a certain class of regression functions. More precisely, the class is defined to be the collection of regression functions such that its (h + 1)th derivative is bounded. The class can be viewed as representing possible departures from an "ideal" simple model and thus describes a model robust setting. The estimates are restricted to be linear and the designs are restricted to be with minimal number of points. The design and estimate sought is minimax for mean square error. The optimal designs for the cases X = {0,(INFIN)) and X = {-1,1}, where X is the place observations can be taken, are obtained. In the second part, we are interested in finding the exact D-optimal design for estimating the coefficients of the polynomial regression of degree n on {a, b}, using the least square estimator. Salaevskii(1966) conjectures that an exact D-optimal design (xi)* distributes observations as evenly as possible among the n + 1 support points of the D-optimal approximate design. A new and simplified proof of Salaevskii's result that the conjecture holds for sufficiently large N is obtained. Also for polynomial regression of degree (LESSTHEQ) 9, Salaevskii's conjecture is proved except for a few cases.
Degree
Ph.D.
Subject Area
Statistics
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