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Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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TL;DR: In this paper, the authors studied the limit distribution of an estimator under such outside-the-model circumstances, where the true hazard rate a(s) is different from the parametric hazard rates.
Abstract: The usual parametric models for survival data are of the following form Some parametrically specified hazard rate a(s, 0) is assumed for possibly censored random life times X, ,X'; one observes only X, = min{X?, ci} and 6& = Ir{X < c,} for certain censoring times c, that either are given or come from some censoring distribution We study the following problems: What do the maximum likelihood estimator and other estimators really estimate when the true hazard rate a(s) is different from the parametric hazard rates? What is the limit distribution of an estimator under such outside-the-model circumstances? How can traditional model-based analyses be made model-robust? Does the model-agnostic viewpoint invite alternative estimation approaches? What are the consequences of carrying out model-based and model-robust bootstrapping? How do theoretical and empirical influence functions generalise to situations with censored data? How do methods and results carry over to more complex models for life history data like regression models and Markov chains?
136 citations
TL;DR: A coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs is presented, which gives a parameterization of the shape that is independent of the mesh, the initial geometry, and the underlying PDE model.
136 citations
TL;DR: In this article, the uniqueness of seminal parametric design concepts and their impact on models of parametric Design Thinking (PDT) are examined through review of key texts and theoretical concepts from early cognitive models up to current models.
136 citations
TL;DR: The experiments that were performed on a bitemporal TerraSAR-X StripMap data set from South West England during and after a large-scale flooding in 2007 confirm the effectiveness of the proposed change detection method and show an increased classification accuracy of the hybrid MRF model in comparison to the sole application of the HMAP estimation.
Abstract: The near real-time provision of precise information about flood dynamics from synthetic aperture radar (SAR) data is an essential task in disaster management. A novel tile-based parametric thresholding approach under the generalized Gaussian assumption is applied on normalized change index data to automatically solve the three-class change detection problem in large-size images with small class a priori probabilities. The thresholding result is used for the initialization of a hybrid Markov model which integrates scale-dependent and spatiocontextual information into the labeling process by combining hierarchical with noncausal Markov image modeling. Hierarchical maximum a posteriori (HMAP) estimation using the Markov chains in scale, originally developed on quadtrees, is adapted to hierarchical irregular graphs. To reduce the computational effort of the iterative optimization process that is related to noncausal Markov models, a Markov random field (MRF) approach is defined, which is applied on a restricted region of the lowest level of the graph, selected according to the HMAP labeling result. The experiments that were performed on a bitemporal TerraSAR-X StripMap data set from South West England during and after a large-scale flooding in 2007 confirm the effectiveness of the proposed change detection method and show an increased classification accuracy of the hybrid MRF model in comparison to the sole application of the HMAP estimation. Additionally, the impact of the graph structure and the chosen model parameters on the labeling result as well as on the performance is discussed.
136 citations
TL;DR: This manuscript revisits the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide, and compares the Multiple Sparse Priors model with the well-known Minimum Norm and LORETA models using the negative variational Free energy for model comparison.
136 citations