The existing estimation techniques for grouped data models can be analyzed as a class of estimators of instrumental variable-Generalized Method of Moments (GMM) type with the matrix of group indicators being the set of instruments. Econometric literature (e.g. Smith, 1997; Newey and Smith, 2004) show that, in some cases of empirical relevance, GMM can have shortcomings in terms of the large sample behaviour of the estimator being different from the finite sample properties. Generalized Empirical Likelihood (GEL) estimators are developed that are not sensitive to the nature and number of instruments and possess improved finite sample properties compared to GMM estimators. In this thesis, with the assumption that the data vector is iid within a group, but inid across groups, we developed GEL estimators for grouped data model having population moment conditions of zero mean of errors in each group. First order asymptotic analysis of the estimators show that they are √N consistent (N being the sample size) and normally distributed. The thesis explores second order bias properties that demonstrate sources of bias and differences between choices of GEL estimators. Specifically, the second order bias depends on the third moments of the group errors and correlation among the group errors and explanatory variables. With symmetric errors and no endogeneity all three estimators Empirical Likelihood (EL), Exponential Tilting (ET) and Continuous Updating Estimator (CUE) yield unbiased estimators. A detailed simulation exercise is performed to test comparative performance of the EL, ET and their bias corrected estimators to the standard 2SLS/GMM estimators. Simulation results reveal that while, with a few strong instruments, we can simply use 2SLS/GMM estimators, in case of many and/or weak instruments, increased degree of endogeneity, or varied signal to noise ratio, bias corrected EL, ET estimators dominate in terms of both least bias and accurate coverage proportions of asymptotic confidence intervals even for a considerably large sample. The thesis includes a case where there are within group dependent data, to assess the consequences of a key assumption being violated, namely the within-group iid assumption. Theoretical analysis and simulation results show that ignoring this feature can result in misleading inference. The proposed estimators are used to estimate the returns to an additional year of schooling in the UK using Labour Force Survey data over 1997-2009. Pooling the 13 years data yields roughly the same estimate of 11.27% return for British-born men aged 25-50 using any of the estimation techniques. In contrast using 2009 LFS data only, for a relatively small sample and many weak instruments, the return to first degree holder men is 13.88% using EL bias corrected estimator, where 2SLS estimator yields an estimate of 6.8%.

Deep learning-based dose prediction is a promising approach to automated radiotherapy planning but carries with it the risk of failing silently when the inputs are highly abnormal compared to the training data. One way to address this issue is to develop a dedicated outlier detector capable of detecting anomalous patient geometries. I examine the potential of so-called generative models to handle this task. These models are promising due to being able to model the distribution of the input data regardless of the downstream task, but they have also been shown to suffer from serious biases when applied to outlier detection. No consensus has been reached regarding the root cause of these biases, or how to address them. I investigate this by attempting to design a variational autoencoder-based outlier detector trained to detect anomalous samples of shapes represented in a binary voxel format. I find the standard procedure application to suffer from severe bias when encountering cropped shapes, leading to systematic misclassification of some outlier patient cases. I overcome this by adopting a segmentation metric as an out-of-distribution metric and show that this outperforms recently proposed general-purpose solutions to the likelihood bias issue. I then benchmark my proposed method on clinical samples and conclude that this approach achieves performance comparable to a one-class support vector machine model that uses handcrafted domain-specific features. / Djupinlärningsbaserad dosprediktion är en mycket lovande metod för att automatiskt generera behandlingsplaner för strålterapi. Djupinlärningsmodeller kan dock endast förväntas fungera på data som är tillräckligt lik träningsdatan, vilket skapar en säkerhetsrisk i kliniska miljöer. Ett möjlig lösning på detta problem är att använda en särskild detektor som klarar av att identifiera avvikande data. I denna uppsats undersöker jag om en generativa djupinlärningsmodell kan användas som en sådan detektor. Generativa modeller är särskilt intressanta för detta ändamål då de är både kraftfulla och flexibla. Dessvärre har generativa modeller visats kunna vilseledas av vissa typer av data. Orsakerna och de underliggande faktorerna till detta har ännu inte identifierats. Jag undersöker denna problematik genom att designa en detektor baserad på en variationell autokodare. Jag upptäcker att den en naiv applikation av denna modell inte är tillräcklig för den kliniska datan, då modellen systematiskt felvärderar beskärda former. Jag löser detta problem genom att nyttja ett modifierat segmenteringsmått som detektionsmått, och visar att denna metod fungerar bättre än mer allmänna lösningar på vilseledningsproblemet. Jag evaluerar metoderna på klinisk data och finner att min metod fungerar lika bra som en en-klass stödvektormaskin som använder sig av handgjorda domänspecifika features.