<div class="csl-bib-body">
<div class="csl-entry">Holynski, T. (2023). Parameter estimation based on differential equations of empirical transforms. In <i>European Meeting of Statisticians 2023 Book of Abstracts</i> (pp. 122–122).</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/187819
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dc.description.abstract
A new class of robust parameter estimators is proposed based on integral transforms of probability distributions, such as the characteristic function or the Laplace transform. In the past, estimators of this type were mostly constructed as minimizers of squared distances between the model transform (of the assumed distribution) and the empirical transform (computed from the sample), e.g. [1], [2] or [3].
Here, instead of using the above distances, we construct estimators by minimizing the L2 norm of ’empirical’ differential equations satisfied by the transforms. Such functionals have been already used in literature but for goodness-of-fit testing, see e.g. [4], [5]. The motivation for applying the equations in the estimation context is that it often leads to
computationally attractive and reliable estimators, having closed-form expressions and being robust to outliers.
We address issues of consistency and asymptotic normality and derive influence functions of the estimators. We show that a good trade-off between robustness and efficiency requires data-driven weight functions in the L2 statistical functionals. In simulations, we study finite sample performance in pure and contaminated models, making comparisons with other kinds of estimators.
en
dc.language.iso
en
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dc.subject
robust parameter estimators
en
dc.title
Parameter estimation based on differential equations of empirical transforms
en
dc.type
Inproceedings
en
dc.type
Konferenzbeitrag
de
dc.description.startpage
122
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dc.description.endpage
122
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dc.type.category
Poster Contribution
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tuw.booktitle
European Meeting of Statisticians 2023 Book of Abstracts