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In this paper, we analyze the effects of the strategic selection of an algebraic subgroup for use in the permutation- or group invariance-based Westfall \& Young maxT multiple testing method. We report the surprising observation that a tiny subgroup can produce a version of the maxT method that dramatically outperforms the method based on entire group or on a large number of Monte Carlo draws. To explain these findings, we characterize the power of the maxT method based on a strategically selected subgroup and the entire group in a Gaussian location model with $p$ tests and $n$ observations. By studying the relative efficiency, we find that the power difference is largest in high dimensional settings where $n^{-1/2} \log p$ is large.

Non-parametric tests based on permutation, rotation or sign-flipping are examples of group-invariance tests. These tests test invariance of the null distribution under a set of transformations that has a group structure, in the algebraic sense. Such groups are often huge, which makes it computationally infeasible to test using the entire group. Hence, it is standard practice to test using a randomly sampled set of transformations from the group. This random sample still needs to be substantial to obtain good power and replicability. We improve upon this standard practice by using a well-designed subgroup of transformations instead of a random sample. The resulting subgroup-invariance test is still exact, as invariance under a group implies invariance under its subgroups. We illustrate this in a generalized location model and obtain more powerful tests based on the same number of transformations. In particular, we show that a subgroup-invariance test is consistent for lower signal-to-noise ratios than a test based on a random sample. For the special case of a normal location model and a particular design of the subgroup, we show that the power improvement is equivalent to the power difference between a Monte Carlo $Z$-test and a Monte Carlo $t$-test.

Primary school students can be difficult to motivate. This can result in low readiness to solve problems that require effort investment, which can in turn result in less effective teaching and learning outcomes. Children’s mindset of intelligence could play a role in their motivation and learning. When a learner has a fixed mindset, intelligence is perceived as something that cannot be changed. While someone who has a growth mindset sees intelligence as something malleable that can be developed. Students who have a fixed mindset are likely to stop learning when they encounter a problem, while students who have a growth mindset are likely to demonstrate perseverance and invest more mental effort. Previous research in cognitive load theory suggests that the effectiveness of certain instructional methods can differ for tasks of varying complexity. It is assumed that the human working memory load is limited thus the complexity of the instructional materials can have an impact on the learning process. Greater complexity requires higher mental effort in the learning process. It is thus possible that differences in complexity can affect learning depending on the learner’s mindset and the corresponding view on effort. The goal of this study was to inform the role of stimulating growth mindset for primary school student learning and improve understanding of its impact on motivation, cognitive load, and performance when solving problems of varying complexity. A randomized controlled experiment was used to test the hypotheses, based on a sample of 118 children from group 7 and 8 (aged 10 to 13) of two primary schools. The study consists of four groups representing two between factors: 1. growth mindset vs. control condition; and 2. low task complexity vs. high task complexity. After participants worked on either a growth mindset or control task, they learnt probabilities through one of two videos that contained an instructional message of either low- or high complexity. The effects of growth mindset and complexity were investigated on attribution, achievement goal orientation, cognitive load and performance. While the growth mindset intervention did significantly improve the experienced growth mindset in the experimental conditions, no evidence was found for an effect on motivation (through attribution and achievement goals), cognitive load, and performance. These findings are comparable with some of the earlier studies on adolescents and university students. The results of the present study indicate that effect of growth mindset intervention remains inconclusive.The complexity intervention did not have an effect on experienced cognitive load, indicating a possibility that the difference between the low and high complexity condition was not big enough to be detected from the current sample, or that self-reported measures might not be an accurate reflection of the actual cognitive load. Although the designs of the mindset materials and the task complexity closely followed theoretical guidelines and previous research, it is possible that the designs can be further improved in future research. Additionally, further research is needed into the effects of growth mindset on children of a lower socioeconomic background, as the current sample consist of mostly children from a higher socioeconomic background.

For a high-dimensional parameter of interest, tests based on quadratic statistics are known to have low power against subsets of the parameter space (henceforth, parameter subspaces). In addition, they typically involve an inverse covariance matrix which is difficult to estimate in high-dimensional settings. I simultaneously address these two issues by proposing a novel test statistic that is large in a conic parameter subspace of interest. This test statistic generalizes the Wald statistic and nests many well-known test statistics. For a given parameter subspace, the statistic is free of tuning parameters and suitable for high-dimensional settings if the subspace is sufficiently small. It can be computed using regularized linear regression, where the type of regularization and the regularization parameters are completely determined by the parameter subspace of interest. I illustrate the statistic on subspaces that consist of sparse or nearly-sparse vectors, for which the computation corresponds to $\ell_0$- and $\ell_1$-regularized regression, respectively.

This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines $\ell_0$- and $\ell_1$-regularization. We compute its solution by adapting a recent methodological innovation made by Bertsimas et al. (2016) for $\ell_0$-regularization in standard linear regression. In a simulation experiment we compare our approach to $\ell_0$-regularization and $\ell_1$-regularization and find that it performs favorably in terms of predictive performance and sparsity. In an application to index tracking we show that our approach can obtain substantially sparser portfolios compared to $\ell_1$-regularization while maintaining a similar tracking performance.

This paper considers the problem of testing many moment inequalities, where the number of moment inequalities ($p$) is possibly larger than the sample size ($n$). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using the maximum $t$ statistic. We observe that such tests can have low power if multiple inequalities are violated. As an alternative, we propose novel randomization tests based on a maximum non-negatively weighted combination of $t$ statistics. We provide a condition guaranteeing size control in large samples. Simulations show that the tests control size in small samples ($n = 30$, $p = 1000$), and often has substantially higher power against alternatives with multiple violations than tests based on the maximum $t$ statistic.

Cardiac surgery with cardiopulmonary bypass leads to impaired perfusion of the microcirculation, which may be an important contributor to postoperative organ dysfunction. This thesis combines clinical and animal studies that aimed to investigate the mechanisms underlying microcirculatory dysfunction in cardiac surgery with cardiopulmonary bypass. Moreover, we aimed to evaluate two treatments strategies for preservation of microcirculatory perfusion during cardiopulmonary bypass : the use of pulsatile flow as compared to the conventional non pulsatile flow during cardiopulmonary bypass and treatment with imatinib in order to reduce vascular leakage by inhibiting endothelial barrier dysfunction.The current thesis has demonstrated that microcirculatory perfusion is impaired during and after cardiac surgery, and this can be attributed mainly to inflammatory endothelial barrier dysfunction and consequent vascular leakage. Concomitant hemodilution may additionally contribute to reduced microvascular perfusion and oxygenation in on-pumpcardiac surgery. We showed that the use of pulsatile flow during cardiopulmonary bypass improves postoperative microvascular perfusion as compared to non pulsatile flow. Imatinib treatment reduced endothelial barrier dysfunction and vascular leakage in our rat model for cardiopulmonary bypass and resulted in preservation of microcirculatory perfusion andoxygenation during and after extracorporeal circulation.Moreover, imatinib treatment resulted in reduced markers ofrenal, pulmonary and intestinal injury after cardiopulmonary bypass. Based on our findings, reduction of vascular leakage and use of pulsatile flow during cardiopulmonary bypass are promising interventions for the prevention of postoperative complications in patients at risk for organ failure following cardiac surgery with cardiopulmonary bypass., La chirurgie cardiaque sous circulation extra-corporelle conduit à une altération de la perfusion de la microcirculation, qui peut contribuer de façon importante à la dysfonction d’organe postopératoire. Cette thèse rassemble des études cliniques et animales, dont le but était d’investiguer les mécanismes expliquant la dysfonction microcirculatoire en chirurgie cardiaque sous circulation extra-corporelle. En outre nous avons eu pour but d’évaluer deux stratégies thérapeutiques pour la préservation de la perfusion microcirculatoire au cours de la circulation extracorporelle : l’utilisation d’un flux pulsé comparativement à un flux non pulsé conventionnel durant la circulation extra-corporelle, et le traitement par imatinib dans le but de réduire la fuite vasculaire en inhibant la dysfonction de la barrière endothéliale. La thèse actuelle a démontré que la perfusion microcirculatoire est altérée durant et après la chirurgie cardiaque, et que ceci peut être attribué principalement à la dysfonction inflammatoire de la barrière endothéliale et à la fuite vasculaire conséquente. L’hémodilution concomitante en chirurgie cardiaque sous circulation extra-corporelle peut s’ajouter et contribuer également à la réduction de la perfusion microcirculatoire et de l’oxygénation. Nous avons montré que l’utilisation d’un flux pulsé durant la circulation extracorporelle améliore la perfusion microcirculatoire en postopératoire comparativement à un flux non-pulsé. Le traitement par imatinib a réduit la dysfonction de la barrière endothéliale et la fuite vasculaire dans notre modèle de circulation extracorporelle sur le rat et a permis de préserver la perfusion microcirculatoire et l’oxygénation durant et après la circulation extra-corporelle. En outre, le traitement par imatinib a permis de diminuer les marqueurs de souffrance rénale, pulmonaire et digestive après circulation extra-corporelle. A partir de nos résultats, la réduction de la fuite vasculaire et l’utilisation d’un flux pulsé durant la circulation extra-corporelle sont des interventions prometteuses pour la prévention des complications postopératoires chez les patients à risque de défaillance d’organe au décours de la chirurgie cardiaque sous circulation extra-corporelle.