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Essays on Inference in Linear Mixed Models

by Peter Kramlinger
Doctoral thesis
Date of Examination:2020-04-28
Date of issue:2020-05-11
Advisor:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Tatyana Krivobokova
Referee:Prof. Dr. Stefan Sperlich
crossref-logoPersistent Address: http://dx.doi.org/10.53846/goediss-7967

 

 

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Abstract

English

This work addresses two aspects of inference in linear mixed models. It is based on two manuscripts, which are provided as addenda. The first manuscript deals with the distinction between marginal and conditional multiple inference, and provides confidence sets useful for testing in each scenario. The second manuscript is concerned with the issue of constructing confidence sets based on the lasso, which hold uniformly over the space of coefficient and covariance parameters.
Keywords: Small Area Estimation; Marginal Inference; Conditional Inference; Multiple testing; simultaneous inference; Lasso; Sparsity; REML; Variance components

German

Diese Arbeit behandelt zwei Aspekte von Inferenz in Gemischten Modellen. Sie basiert auf Manuskripten, welche im Anhang bereitgestellt sind. Im ersten Teil wird zwischen bedingter und marginaler multipler Inferenz unterschieden und Konfidenzbereiche zum Testen von statistischen Hypothesen hergeleitet. Im zweiten Teil werden Konfidenzbereiche hergeleitet, welche auf dem Lasso beruhen. Diese haben uniforme Bedeckungswahrscheinlichkeiten über dem Raum der Koeffizienten- und Kovarianzparameter.
 

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