Construction of restricted D-optimal designs for polynomial regression models /
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| Other Authors: | , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1989.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | Experimental situations where replicate values of x are not feasible and the design space is restricted to N equally spaced points are considered. Under these restrictions D-optimal designs for selecting the n distinct values of x in polynomial regression models are investigated. A sequential algorithm is developed and its performance is evaluated for small values of N and n where the restricted D-optimal designs can be found by an exhaustive search algorithm. The sequential algorithm gives excellent performance for the cases considered both in terms of efficiency and computing time. A heuristic near-optimal design is proposed and its performance is compared to uniform -spacing, restricted .D-optimal and approximate D -optimal designs. The improvement of the near-optimal design over the uniform-spacing design is substantial for a wide range of values of N and n. For small values of N, efficiency of the near-optimal design is shown to be one or close to one. For large values of N, the determinant of the approximate D-optimal design is used to obtain a lower bound for the efficiency of the near-optimal design. Again, efficiency of the near-optimal design is shown to be close to one for large N. Efficiency of the near-optimal design based upon misspecified polynomial regression models is investigated. An analytic expression for relative efficiency of near-optimal designs based upon a misspecified quadratic regression model with respect to uniform-spacing designs when simple linear regression is true is derived. Relative efficiency of near-optimal designs based on various other model misspecifications are tabulated. Superiority of near-optimal designs (based on misspecified models) over uniform-spacing designs is demonstrated for a wide range of N, n and p values. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Statistics." |
| Physical Description: | x, 118 leaves ; 29 cm |
| Bibliography: | Includes bibliographical references. |