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| Author | : Abdelaati Daouia |
| Publisher | : |
| Total Pages | : |
| Release | : 2022 |
| Genre | : |
| ISBN | : |
| Author | : Liang Peng |
| Publisher | : Academic Press |
| Total Pages | : 182 |
| Release | : 2017-08-11 |
| Genre | : Mathematics |
| ISBN | : 012804750X |
Heavy tailed data appears frequently in social science, internet traffic, insurance and finance. Statistical inference has been studied for many years, which includes recent bias-reduction estimation for tail index and high quantiles with applications in risk management, empirical likelihood based interval estimation for tail index and high quantiles, hypothesis tests for heavy tails, the choice of sample fraction in tail index and high quantile inference. These results for independent data, dependent data, linear time series and nonlinear time series are scattered in different statistics journals. Inference for Heavy-Tailed Data Analysis puts these methods into a single place with a clear picture on learning and using these techniques. Contains comprehensive coverage of new techniques of heavy tailed data analysis Provides examples of heavy tailed data and its uses Brings together, in a single place, a clear picture on learning and using these techniques
| Author | : Jayakrishnan Nair |
| Publisher | : Cambridge University Press |
| Total Pages | : 266 |
| Release | : 2022-06-09 |
| Genre | : Mathematics |
| ISBN | : 1009062964 |
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
| Author | : S. Y. Novak |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1999 |
| Genre | : |
| ISBN | : |
| Author | : Victor Chernozhukov |
| Publisher | : |
| Total Pages | : 40 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional value-at-risk, production efficiency, and adjustment bands in (S, s) models. In this paper we provide feasible inference tools for extremal conditional quantile models that rely upon extreme value approximations to the distribution of self-normalized quantile regression statistics. The methods are simple to implement and can be of independent interest even in the non-regression case. We illustrate the results with two empirical examples analyzing extreme fluctuations of a stock return and extremely low percentiles of live infants' birth weights in the range between 250 and 1500 grams.
| Author | : Robert Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 560 |
| Release | : 1998-10-26 |
| Genre | : Mathematics |
| ISBN | : 9780817639518 |
Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
| Author | : Laurens de Haan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 421 |
| Release | : 2007-12-09 |
| Genre | : Mathematics |
| ISBN | : 0387344713 |
Focuses on theoretical results along with applications All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion Concentration is on the probabilistic and statistical aspects of extreme values Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity
| Author | : Wei Liu |
| Publisher | : CRC Press |
| Total Pages | : 292 |
| Release | : 2010-10-19 |
| Genre | : Mathematics |
| ISBN | : 9781439828106 |
Simultaneous confidence bands enable more intuitive and detailed inference of regression analysis than the standard inferential methods of parameter estimation and hypothesis testing. Simultaneous Inference in Regression provides a thorough overview of the construction methods and applications of simultaneous confidence bands for various inferentia
| Author | : Natalia Markovich |
| Publisher | : John Wiley & Sons |
| Total Pages | : 336 |
| Release | : 2008-03-11 |
| Genre | : Mathematics |
| ISBN | : 9780470723593 |
Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
| Author | : Victor Chernozhukov |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
This paper develops a theory of high and low (extremal) quantile regression: the linear models, estimation, and inference. In particular, the models coherently combine the convenient, flexible linearity with the extreme-value-theoretic restrictions on tails and the general heteroscedasticity forms. Within these models, the limit laws for extremal quantile regression statistics are obtained under the rank conditions (experiments) constructed to reflect the extremal or rare nature of tail events. An inference framework is discussed. The results apply to cross-section (and possibly dependent) data. The applications, ranging from the analysis of babies' very low birth weights, (S,s) models, tail analysis in heteroscedastic regression models, outlier-robust inference in auction models, and decision-making under extreme uncertainty, provide the motivation and applications of this theory.
