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There was a problem with saving your item s for later. You can go to cart and save for later there. Average rating: 0 out of 5 stars, based on 0 reviews Write a review. Tell us if something is incorrect. Out of stock. Delivery not available. Pickup not available. Presented in honor of Ursula Gather's 60th birthday this book deals with modern topics in the field of robust statistical methods, especially for time series and regression analysis, and with statistical methods for complex data structures.
About This Item We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. See our disclaimer. Robustness and Complex Data Structures. Specifications Publisher Springer. Customer Reviews.
Write a review. See any care plans, options and policies that may be associated with this product. Email address. Please enter a valid email address. In case of change s in the model being detected the further task is also to estimate the time of change and other parameters of the model in the periods where the model is stable. Various robust procedures for the above formulated problems are presented and discussed. For data streams which are distorted by noise and outliers, it is a basic goal to extract the unknown underlying signal carrying the relevant information in real time.
We review procedures for real time signal extraction or filtering, which are based on robust location and regression estimators applied to moving time windows. Since Repeated Median RM regression has turned out to have good properties for online signal extraction, we introduce several recently developed filters based on RM regression.
In particular, we focus on RM-based filters with data-adaptive selection of the window width n. These filters choose n —which can have a large influence on the resulting signal estimation—according to the current data situation at each time point. We also present multivariate RM-based filters for signal extraction from multivariate data streams.
Robustness in time series analysis is an important issue. A motivation for robust frequency domain analysis can be taken from medical application: Short-term heart rate variability recordings are usually analyzed in the frequency domain. The heart rate variability is assessed by estimating the spectral density function of the tachogram series.
It is well known that classical spectral density estimates are prone to outlying observations, hence, robustness is an issue. The presented multi-step procedure based on robust filtering is insensitive to outliers, and therefore provides fully automated signal processing which will facilitate reliable and reproducible heart rate variability analysis with minimal operator input. Moreover, it can also be used to identify and mark outlying observations. Problems of statistical forecasting of time series under distortions of hypothetical models are considered. Mathematical descriptions of typical distortions are given.
New robust forecasting statistics are constructed. The theoretical results are illustrated by numerical experiments. The purpose of this contribution is to review outliers in both univariate and multivariate time series.
Robustness and Complex Data Structures
The usual outlier types are presented in several frameworks including linear and nonlinear time series models. The key issues regarding identification of outliers and estimation of their effects in different settings are summarized. The finite sample distribution of many nonparametric methods from statistical learning theory is unknown because the distribution P from which the data were generated is unknown and because there often exist only asymptotical results on the behaviour of such methods.
The goal of this contribution is to show that bootstrap approximations of an estimator which is based on a continuous operator from the set of Borel probability distributions defined on a compact metric space into a complete separable metric space is stable in the sense of qualitative robustness. As a special case it is shown that, under certain regularity conditions, bootstrap approximations for many general support vector machines SVM are qualitatively robust, both for the real-valued SVM risk and for the SVM itself.
The required regularity conditions involve the loss function and the kernel, but not the unknown distribution P. Hence, these conditions are verifiable in advance and are not data dependent. Investigating time is not restricted to time series analysis, where from a sequence of equidistant measurements the value of the next measurement is predicted.
In contrast, many applications have to cope with very large collections of time series data. The tasks range from regression and classification to detecting patterns in the data. By several case studies stemming from several years of research, this chapter illustrates the diversity of temporal phenomena handled in machine learning and data mining on the basis of very large data sets.
The path leads from time series classification to the analysis of streaming data.
Robustness and Complex Data Structures Festschrift in Honour of Ursula Gather by Becker & Claudia
A recurrent theme is the appropriate representation, feature extraction, and feature selection for high performance learning. In this contribution we analyze the interplay between correlation, tail dependence and diversification between risks which has a great impact on the calculation of the Solvency Capital Requirement under the Solvency II directive.
The analysis shows that the prevailing assumption of an economic relationship between diversification and correlation or stochastic dependence is misleading under the risk measure VaR Value at Risk used under Solvency II and can lead to an underestimation of the necessary economic capital. Most researchers want evidence for the direction of an effect, not evidence against a point null hypothesis.
Such evidence is ideally on a scale that is easily interpretable, with an accompanying standard error.
Further, the evidence from identical experiments should be repeatable, and evidence from independent experiments should be easily combined, such as required in meta-analysis. Such a measure of evidence exists and has been shown to be closely related to the Kullback—Leibler symmetrized distance between null and alternative hypotheses for exponential families. Here we provide more examples of the latter phenomenon, for distributions lying outside the class of exponential families, including the non-central chi-squared family with unknown non-centrality parameter.
With graphical Markov models, one can investigate complex dependences, summarize some results of statistical analyses with graphs and use these graphs to understand implications of well-fitting models. The models have a rich history and form an area that has been intensively studied and developed in recent years.