Publisher:

Chapman & Hall/CRC

Number of Pages:

373

Price:

99.95

ISBN:

9781439835746

Date Received:

Tuesday, January 10, 2012

Reviewable:

No

Reviewer Email Address:

Series:

Monographs on Statistics and Applied Probability 122

Publication Date:

2012

Format:

Hardcover

Audience:

Category:

Monograph

**IntroductionDistribution of Extremes**

"Blocks" and "Runs" Approaches

Method of Recurrent Inequalities

Proofs

Maximum of Partial Sums

Erdős–Rényi Maximum of Partial Sums

Basic Inequalities

Limit Theorems for MPS

Proofs

Extremes in Samples of Random Size

Maximum of a Random Number of r.v.s

Number of Exceedances

Length of the Longest Head Run

Long Match Patterns

Poisson Approximation

Total Variation Distance

Method of a Common Probability Space

The Stein Method

Beyond Bernoulli

The Magic Factor

Proofs

Compound Poisson Approximation

Limit Theory

Accuracy of CP Approximation

Proofs

Exceedances of Several Levels

CP Limit Theory

General Case

Accuracy of Approximation

Proofs

Processes of Exceedances

One-level EPPE

Excess Process

Complete Convergence to CP Processes

Proofs

Beyond Compound Poisson

Excess Process

Complete Convergence

Proofs

Statistics of Extremes

Inference on Heavy Tails

Heavy-tailed distributions

Estimation Methods

Tail Index Estimation

Estimation of Extreme Quantiles

Estimation of the Tail Probability

Proofs

Value-at-Risk

Value-at-Risk and Expected Shortfall

Traditional Methods of VaR Estimation

VaR and ES Estimation from Heavy-Tailed Data

VaR over Different Time Horizons

Technical Analysis of Financial Data

Extremal Index

Preliminaries

Estimation of the Extremal Index

Proofs

Normal Approximation

Accuracy of Normal Approximation

Stein’s Method

Self-Normalized Sums of r.v.s

Proofs

Lower Bounds

Preliminary Results

Fréchét–Rao–Cramér Inequality

Information Index

Continuity Moduli

Tail Index and Extreme Quantiles

Proofs

Appendix

Probability Distributions

Properties of Distributions

Probabilistic Identities and Inequalities

Distances

Large Deviations

Elements of Renewal Theory

Dependence

Point Processes

Slowly Varying Functions

Useful Identities and Inequalities

References

Publish Book:

Modify Date:

Monday, June 18, 2012

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