Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 7 of 7 for “"Oracle inequality"”.
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Theory and Algorithms for Penalization, Graphical Models, and Surrogate Marker Evaluation
In this dissertation, we study three problems: oracle inequality in high-dimensional statistics theory, graphical models, and surrogate measures in clinical trials. First, we introduce a general slow rate bound for maximum regularized likelihood estimators in Kullback-Leibler divergence. The result …
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Wavelet Thresholding for Non (Necessarily) Gaussian Noise
Soon after the discovery of orthonormal wavelets, in particular the <br>compactly supported ones, <br>these wavelets have been used for non-parametric function estimation. <br>In the literature, two main models are present. In the first model, <br>the target functions are members of some smoothness …
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Essays on Adaptive Methods for Inference and Prediction under Dependence
… patterns (e.g., exposure mappings). We establish oracle inequalities and corresponding adaptive rates for the estimation of the interference function. Such estimates lead to two different estimators ($\hat{\tau}^{OR}$ and $\hat{\tau}^{DR}$) for the average direct treatment effect on the treated. …
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Polynomial methods in statistical inference: Theory and practice
… optimality of the proposed procedure, as well as oracle inequality in misspecified models. These results can also be viewed as provable algorithms for generalized method of moments which involves non-convex optimization and lacks theoretical guarantees.
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Non-asymptotic bounds for prediction problems and density estimation.
This dissertation investigates the learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary classification problem in the framework of …
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Optimal estimation in high-dimensional and nonparametric models
… with minimal variance among all unbiased oracle-type estimators. Our approach is based on a Poisson point process model and as an ingredient, we prove that the convex hull is a sufficient and complete statistic. No hypotheses on the boundary of the convex set are imposed. In a numerical …