The Fundamentals of Heavy Tails

The Fundamentals of Heavy Tails
Author: Jayakrishnan Nair
Publisher: Cambridge University Press
Total Pages: 266
Release: 2022-06-09
Genre: Mathematics
ISBN: 1009062964

Download The Fundamentals of Heavy Tails Book in PDF, Epub and Kindle

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.

Heavy-Tailed Distributions and Robustness in Economics and Finance

Heavy-Tailed Distributions and Robustness in Economics and Finance
Author: Marat Ibragimov
Publisher: Springer
Total Pages: 131
Release: 2015-05-23
Genre: Business & Economics
ISBN: 3319168770

Download Heavy-Tailed Distributions and Robustness in Economics and Finance Book in PDF, Epub and Kindle

This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. A central theme is that of (non-)robustness, i.e., the fact that the presence of heavy tails can either reinforce or reverse the implications of a number of models in these fields, depending on the degree of heavy-tailed ness. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations. Several recently developed robust inference approaches are discussed and illustrated, together with applications.

Subsampling

Subsampling
Author: Dimitris N. Politis
Publisher: Springer Science & Business Media
Total Pages: 359
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461215544

Download Subsampling Book in PDF, Epub and Kindle

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.

Statistical Inference as Severe Testing

Statistical Inference as Severe Testing
Author: Deborah G. Mayo
Publisher: Cambridge University Press
Total Pages: 503
Release: 2018-09-20
Genre: Mathematics
ISBN: 1108563309

Download Statistical Inference as Severe Testing Book in PDF, Epub and Kindle

Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.

Fat-tailed Distributions

Fat-tailed Distributions
Author: Roger M. Cooke
Publisher:
Total Pages:
Release: 2014
Genre: MATHEMATICS
ISBN: 9781119054207

Download Fat-tailed Distributions Book in PDF, Epub and Kindle

Statistical Inference via Data Science: A ModernDive into R and the Tidyverse

Statistical Inference via Data Science: A ModernDive into R and the Tidyverse
Author: Chester Ismay
Publisher: CRC Press
Total Pages: 461
Release: 2019-12-23
Genre: Mathematics
ISBN: 1000763463

Download Statistical Inference via Data Science: A ModernDive into R and the Tidyverse Book in PDF, Epub and Kindle

Statistical Inference via Data Science: A ModernDive into R and the Tidyverse provides a pathway for learning about statistical inference using data science tools widely used in industry, academia, and government. It introduces the tidyverse suite of R packages, including the ggplot2 package for data visualization, and the dplyr package for data wrangling. After equipping readers with just enough of these data science tools to perform effective exploratory data analyses, the book covers traditional introductory statistics topics like confidence intervals, hypothesis testing, and multiple regression modeling, while focusing on visualization throughout. Features: ● Assumes minimal prerequisites, notably, no prior calculus nor coding experience ● Motivates theory using real-world data, including all domestic flights leaving New York City in 2013, the Gapminder project, and the data journalism website, FiveThirtyEight.com ● Centers on simulation-based approaches to statistical inference rather than mathematical formulas ● Uses the infer package for "tidy" and transparent statistical inference to construct confidence intervals and conduct hypothesis tests via the bootstrap and permutation methods ● Provides all code and output embedded directly in the text; also available in the online version at moderndive.com This book is intended for individuals who would like to simultaneously start developing their data science toolbox and start learning about the inferential and modeling tools used in much of modern-day research. The book can be used in methods and data science courses and first courses in statistics, at both the undergraduate and graduate levels.

Optimal Statistical Inference in Financial Engineering

Optimal Statistical Inference in Financial Engineering
Author: Masanobu Taniguchi
Publisher: CRC Press
Total Pages: 379
Release: 2007-11-26
Genre: Business & Economics
ISBN: 1420011030

Download Optimal Statistical Inference in Financial Engineering Book in PDF, Epub and Kindle

Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively des

Machine Learning and Knowledge Extraction

Machine Learning and Knowledge Extraction
Author: Andreas Holzinger
Publisher: Springer Nature
Total Pages: 552
Release: 2020-08-19
Genre: Computers
ISBN: 3030573214

Download Machine Learning and Knowledge Extraction Book in PDF, Epub and Kindle

This book constitutes the refereed proceedings of the 4th IFIP TC 5, TC 12, WG 8.4, WG 8.9, WG 12.9 International Cross-Domain Conference, CD-MAKE 2020, held in Dublin, Ireland, in August 2020. The 30 revised full papers presented were carefully reviewed and selected from 140 submissions. The cross-domain integration and appraisal of different fields provides an atmosphere to foster different perspectives and opinions; it will offer a platform for novel ideas and a fresh look on the methodologies to put these ideas into business for the benefit of humanity. Due to the Corona pandemic CD-MAKE 2020 was held as a virtual event.

Applying Contemporary Statistical Techniques

Applying Contemporary Statistical Techniques
Author: Rand R. Wilcox
Publisher: Gulf Professional Publishing
Total Pages: 688
Release: 2003-01-06
Genre: Mathematics
ISBN: 9780127515410

Download Applying Contemporary Statistical Techniques Book in PDF, Epub and Kindle

Applying Contemporary Statistical Techniques explains why traditional statistical methods are often inadequate or outdated when applied to modern problems. Wilcox demonstrates how new and more powerful techniques address these problems far more effectively, making these modern robust methods understandable, practical, and easily accessible. Highlights: * Assumes no previous training in statistics * Explains when and why modern methods provide more accurate results * Provides simple descriptions of when and why conventional methods can be highly unsatisfactory * Covers the latest developments on multiple comparisons * Includes recent advances in risk-based methods * Features many illustrations and examples using data from real studies * Describes and illustrates easy-to-use s-plus functions for applying cutting-edge techniques "The book is quite unique in that it offers a lot of up-to-date statistical tools. No other book at this level comes close in this aspect." Xuming He -University of Illinois, Urbana