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Robustness of estimation based on empirical transforms

Campbell, Edward (1992) Robustness of estimation based on empirical transforms. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.86151) (KAR id:86151)

Language: English

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The robustness of certain model-fitting procedures, based on statistical transforms, is investigated using the Influence Function. Our discussion is in two parts. In the first, we focus on estimateing the parameters of particular distributions, given independent and identically distributed realizations. We then move on, in the second part, to discuss the fitting of stochastic models.

In this latter context the approach baesd on transforms, such as the Laplace transform, offers the possibility of explicit parameter estimation. This is in obvious contrast to the more usual situation where only a numerical solution is possible. It was shown by Kemp & Kemp (1987), in a two-parameter example, that only a one-dimensional search was required to produce well-defined estimators. This phenomenon was noted earlier by Morgan (1982), and provides further motivation for transform methods. We generalize the result, and provide an example where a three-dimensional search can be reduced to a line search. With this in mind, we consider the fitting of stochastic models in some detail, employing the standard technique of ordinary least-squares as a bench-mark in this work.

The central theme of this thesis is, however, the robustness of such methods. To this end, we develop a powerful and flexible influence theory in the context of non-indexed random variables. These developments allow us to make concrete statements about the robustness of procedures based on transforms. We show that an analogous treatment is possible for the indexed case, allowing useful qualitative information about parameter estimators to be gathered.

Item Type: Thesis (Doctor of Philosophy (PhD))
DOI/Identification number: 10.22024/UniKent/01.02.86151
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 09 February 2021 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives ( licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies ( If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at and we will seriously consider your claim under the terms of our Take-Down Policy (
Uncontrolled keywords: Statistics
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 29 Oct 2019 16:30 UTC
Last Modified: 22 Nov 2021 09:45 UTC
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