In statistical inference, it is important to estimate the parameters of a regression model in such a way that the variances of the estimates are as small as possible. Motivated by this fact, we have tried to address this important problem using optimal design theory.
We start with some optimal design theory and determine the optimality conditions in terms of a directional derivative. We construct the optimal designs for minimizing variances of the parameter estimates in two ways. The first one is the analytic approach, in which we derive the derivatives of our criterion and solve the resulting equations. In another approach, we construct the designs using a class of algorithms.
We also construct designs for minimizing the total variance of some parameter estimates. This is motivated by a practical problem in Chemistry. We attempt to improve the convergence of the algorithm by using the properties of the directional derivatives. / October 2016
| Identifer | oai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/31814 |
| Date | 19 September 2016 |
| Creators | Chen, Manqiong |
| Contributors | Saumen Mandal （Statistics）, Saumen Mandal (Statistics) Aerambamoorthy Thavaneswaran (Statistics) Yang Zhang (Mathematics) |
| Source Sets | University of Manitoba Canada |
| Detected Language | English |
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