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Linear regression models are very popular among users as they allow an intuitive interpretation of the dependencies between an outcome variable and explanatory variables. However, to avoid false conclusions from such models, any statistical inference should be backed up by a goodness-of-fit test. These tests check whether the hypothesised class of possible regression functions has been adequately chosen.
In this work, goodness-of-fit tests for univariate linear regression models based on the asymptotic distribution of residual CUSUM processes are studied. In the literature, a distinction is made between random designs and fixed designs when studying such goodness-of-fit tests. We prove that for each of these two scenarios (random and fixed design) there is a corresponding uniform design, we examine similarities and differences between these two scenarios, and prove that, when it comes to goodness-of-fit tests in in linear regression models based on the asymptotic distribution of residual CUSUM processes, one can assume without loss of generality a generic linear regression model.
Furthermore, a geometric interpretation of residual CUSUM limit processes as projections on certain reproducing kernel Hilbert spaces is given, the effect of heteroscedastic regression errors on residual CUSUM limit processes is investigated, and an interpretation of the Khmaladze maratingale transformation as a continuous-time recursive least squares method is made explicit.
Finance without foundations
(2022)
This thesis examines the role of financial inclusion by way of access to formal financial services such as savings, credit, transfers and payments, in supporting the lives of refugees in protracted displacement in Jordan. It asks if such access enables smoother financial and livelihood transitions as refugees arrive and integrate into their new environments in host countries. It critically evaluates the narrative presented by humanitarian actors supporting financial inclusion as a marketled intervention to support refugee self-reliance. It argues that the limited provision of financial services through mobile wallets and micro-credit is not sufficient to financially integrate refugees. Above all, it demonstrates through the in-depth qualitative research in Jordan that in a context where refugees’ livelihoods are constrained due to a lack of foundational economic rights, financial services can only marginally improve their lives by making it more convenient to receive remittances and humanitarian transfers.
The research is embedded in a larger project called “Finance in Displacement: Exploring and strengthening financial lives of forcibly displaced persons” (FIND), which was initiated in 2019 as a collaboration between the Katholische Universität Eichstätt-Ingolstadt, the Tufts University, and the International Rescue Committee. The project was supported by the German Federal Ministry for Economic Cooperation and Development (BMZ).