Title Promoter Affiliations Abstract "Robust bootstrap inference for linear models with non i.i.d. errors or dependent observations" "Stefan Van Aelst" "Department of Applied Mathematics, Computer Science and Statistics" "Develop fast robust bootstrap inference for robust regression with dependent observations or heteroscedastic or skew errors. Develop more efficient robust estimators such as S-estimators for these more complex linear models by modeling explicitly the heteroscedasticity or skewness, and investigate the properties of the resulting estimators. Develop fast and robust bootstrap inference for these new robust estimators." "Financing of start-ups in Flanders: determinants of the start-up capital and the use of bootstrap financing." "Eddy Laveren" "Accountancy and Finance" "New start-ups lack prior history or lack reputation and are associated with a high failure risk. Nevertheless, a future entrepeneur needs to find a sufficient amout of capital in order to be able to start a new venture. The aim of this study is to identify the determinants of both the initial start-up capital as well as the use of bootstrap financing in newly founded ventures. Moreover, this study will investigate the impact of bootstrap financing on the new venture's performance." "Bootstrap-based corrections for LS and IV estimators in dynamic panels" "Gerdie Everaert" "Department of Social economics" "The LSDV estimator is known to be strongly biased in dynamic panels. The goal of this project is to investigate the performance of a boostrap-based bias correction for models with higher order dynamics and a vector of (endogenous) explanatory variables. Furthermore, we explore alternative ways to estimate the long-term impact. Finally, we want to apply our findings to the convergence debate." "Bootstrapping operations in language acquisition: a computational psycholinguistic approach." "Steven Gillis" "Centre for Computational Linguistics, Psycholinguistics and Sociolinguistics (CLiPS)" "The acquisition of abstract linguistic categories is investigated. Computational models of bootstrapping operations are constructed in order to investigate how knowledge from one domain can be instrumental in acquiring knowledge of another domain. In our simulations the language addressed to very young children is used in an attempt to elucidate how grammatical categories and grammatical gender are acquired given a combination of distributional, phonological and morphological bootstrapping." "Robust inference techniques based on resampling" "Stefan Van Aelst" "Statistics and Risk, Statistics and Data Science" "Linear regression is the most famous type of regression analysis in statistics. A statistical analysis of a linear regression model usually begins with estimation of the regression coefficients and continues with measuring the accuracy of the estimators. Unfortunately, it is well known that a traditional statistical analysis based on the least squares principle is very sensitive to outliers in the data. Although many robust estimators have been proposed to control the effect of outliers, robust inference techniques have remained more scarce. Therefore, the main goal of this thesis is to investigate robust inference techniques. For the approach in this thesis, the key concept for the development of robust inference is the fast and robust resampling methodology. Instead of applying standard resampling techniques such as bootstrapping and subsampling, a resampling distribution is generated by calculating a fast and robust resampling estimator for a large number of resamples. The resulting resampling distribution is robust against outliers and can also be computed extremely fast, as opposed to the original resampling algorithm. Inference based on fast and robust resampling is considered for seemingly unrelated regression models and for generalized linear models.Seemingly unrelated regression models generalize linear regression models with normally distributed errors by considering multiple regression equations that are linked by contemporaneously correlated disturbances. MM-estimators are introduced to obtain estimators that have a high breakdown point and a high normal efficiency. A fast and robust bootstrap procedure is then developed to obtain robust inference for these estimators. Confidence intervals for the model parameters as well as hypothesis tests for linear restrictions of the regression coefficients in seemingly unrelated regression models are constructed. Moreover, in order to evaluate the need for a seemingly unrelated regression model, a robust procedure is proposed to test for the presence of correlation among the disturbances. The performance of the fast and robust bootstrap inference is evaluated empirically in simulation studies and illustrated on real data.MM-estimators for seemingly unrelated regression models are applied in the framework of stochastic loss reserving for general insurance, as a robust alternative to the general multivariate chain ladder method. The chain ladder method is a widely used technique to forecast the reserves that an insurance company will be liable to pay in the event of a claim. To make predictions for multiple run-off triangles simultaneously, a general multivariate chain ladder method has been proposed that takes into account contemporaneous correlations and structural connections between different run-off triangles. With the robust methodology it is possible to detect which claims have an abnormally large influence on the reserve estimates. A simulation design is introduced to generate artificial multivariate run-off triangles and the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles is illustrated. By generating contaminated data the sensitivity of the traditional chain ladder method and the good performance of the robust method is shown. The analysis of a portfolio from practice makes clear that the robust method can provide better insight in the structure of the data.Finally, robust model selection inspired by the fast and robust resampling methodology is introduced for generalized linear models. Selecting the optimal model from a set of competing models is an essential task in statistics. Particular attention is paid to a robust model selection criterion that combines goodness of fit and a measure of prediction. The prediction loss is estimated by using resampling techniques. In addition to case bootstrapping, also error bootstrapping and subsampling algorithms are considered. To reduce the computational burden, a modified fast and robust resampling method is proposed. It is shown that this modification still yields a consistent model selection criterion, in the sense that the optimal model is identified with probability one as the sample size grows to infinity. The performance of the proposed methodology is evaluated empirically by a simulation study and illustrated on real data examples." "Bias correcting panel data estimators in dynamic models with cross-sectional dependence and endogeneity" "Gerdie Everaert" "Department of Social economics" "The FE and CCEP estimators show considerable bias in dynamic models. Many corrections have been devised for FE, but none are applicable to case of endogenous regressors. We address this issue with the bootstrap method. The CCEP estimator is essential under cross-section dependence but has not yet been bias corrected. Such corrections (analytical and bootstrap-based) constitute our second research goal." "Post-quantum cryptography" "Ingrid Verbauwhede" "Computer Security and Industrial Cryptography (COSIC)" "Homomorphic encryption allows computations on encrypted data without revealing its content. Although it has a wide range of applications in privacy preserving data processing, current techniques are impractical due to extreme overheads compared to unencrypted computations. The PhD aims to reduce the computational cost of homomorphic encryption at three levels: algorithmic improvements, software and hardware implementations and applications." "Asymptotic theory of debiased regularized M-estimators" "Gerda Claeskens" "Operations Research and Statistics Research Group (ORSTAT) (main work address Leuven)" "Regression coefficient estimation by regularized estimators such as the Lasso, introduces bias and its selection of coefficients makes classical inference methods inappropriate. Concerning debiasing the regularized estimator, recent literature focuses mostly on the case of the least squares loss, leaving other loss functions such as the quantile loss underexplored. My research proposal mainly investigates the general class of debiased regularized M-estimators. I develop a theoretical study and a computational approach for generating componentwise confidence intervals for coefficients in high-dimensional linear models. A bootstrap method using debiased l_1-regularized M-estimators is studied, and extended towards l_1regularized model averaged and composite M-estimators. Quantile regression is an example. A new choice of weights for model averaged and composite estimation is proposed by minimizing an analytical expression for the asymptotic variance of such debiased l_1-regularized M-estimators. A bootstrap procedure is to be developed to study the distribution of the estimated weights. The efficiency of such estimators using random weights will be compared with similar estimators using deterministic weights. Further, since the debiased l_1-regularized M-estimators are only asymptotically unbiased, I consider a double-debiasing procedure to further improve the sample size requirements for these estimators to possess good theoretical properties. " "Robust techniques for functional data and generalized linear models" "Tim Verdonck" "Statistics and Risk, Statistics and Data Science" "Robust estimators are indispensable tools in statistics. Frequently, a (small) part of the data sample follows a different pattern as the majority of the data or even no pattern at all. Such atypical observations are called outliers. They may be simple gross errors such as measurement errors or copying mistakes. However, they may also be observations governed by different laws or indicate subgroups or structures in the data sample. Two different frameworks with different areas of application are studied. Firstly, robust techniques for functional data are investigated. This type of data, popularized by advances in data gathering, has led to a new field of study in statistics. New techniques for the detection of outliers are proposed, such as the Centrality-Stability Plot, the Functional Outlier Map, and heatmaps. These are based on statistical depth functions and distance measures derived from them. The techniques are illustrated on both univariate and multivariate functional data. Moreover, functional data defined on a multivariate domain, such as fluorescence excitation-emission spectra or video data are studied. Robust supervised classification of functional data is discussed in the third chapter. A new classification procedure based on the DistSpace transform is proposed,  which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines affine invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with both real and simulated data. A second part of the thesis concerns Generalized Linear Models or GLMs, a unified regression framework for response variables belonging to the exponential family. This family encompasses a broad class of popular distributions such as the normal, Poisson, binomial and gamma distribution. Moreover, GLMs only assume a linear relation, up to transformation, between the predictors and the mean of the response variable.Chapter 4 discusses a problem in actuarial sciences. More specifically, we consider the challenge insurers face when estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A  well-known and widely used technique in this context is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component, one may apply GLMs to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive.  A popular alternative approach to obtain inference  is to use the bootstrap technique. However, the standard procedures are sensitive to the possible presence of outliers. These atypical observations, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Several robust bootstrap procedures are investigated in the claims reserving framework comparing their performance on both simulated and real data. Chapter 5 deals with a phenomenon frequently occurring when analyzing data with GLMs. Real data often display a larger or smaller variability than expected under the prescribed GLM. This extra deviation around the mean, or lack thereof in case of underdispersion, may be constant across observations but may equally well depend on a set of predictors. Accounting for this varying dispersion is critical for several reasons. Firstly, correct confidence intervals for the regression coefficients governing the mean depend on the dispersion effects. Secondly, ignoring dispersion may result in a loss of efficiency in the estimation of the mean coefficients. Lastly, the dispersion model itself may be the main focus of interest. We propose a robust estimator for the joint modeling of mean and dispersion effects in the context of GLMs. Our methodology does not suppose constant dispersion but models both mean and dispersion behavior based on a possibly different set of predictors. As such, the proposed methodology is highly flexible. We derive theoretical properties of the estimator and discuss the problem of robust inference. The good performance of the estimator is shown on both simulated and real data. " "Multilevel synthesis of single-case experimental data: further developments and empirical validation." "Wim Van Den Noortgate" "Faculty of Psychology and Educational Sciences, Kulak Kortrijk Campus" "In single-case or single-subject designs (SSED), individual cases are measured repeatedly under different conditions, in order to assess the effect of the condition. Recently, multilevel models were proposed to combine the results of SSED studies, resulting in more general or detailed conclusions. The purpose of the proposed research is to empirically investigate the multilevel approach, using both real data and simulation studies. The research will entail several studies designed to address major complications encountered when syntesizing results from SSED research. A fist set is designed for synthesizin results from SSED studies with outcomes in the same metric. The initial study will focus on the basis three-level model for the meta-analysis of SSED studies with the same outcome. A series of additional studies will target complications encountered in the synthesis of SSED studies' results, including: autocorrelation, count data outcomes, designs with multiple outcomes and/or settings, models with nonlinear growth trajectories, and the use of bootstrapping estimation techniques. The second set will assess synthesis of standardized raw data and effect sizes necessary for meta-analyzing results from SSED studies employing outcomes on different metrics."