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<br/></p><p>Sidney I. Resnick<br/>《Heavy-Tail Phenomena<br/>Probabilistic and Statistical Modeling》</p><p>The structure of the book<br/>There is an introductory chapter to describe the flavor and applicability of the subject.<br/>Then there are two chapters termed crash courses: one on regular variation and the other<br/>on weak convergence. These chapters contain essential material that could have been<br/>relegated to appendices; however, you should go through them where they are placed<br/>in the book. If you know the material, move quickly. Otherwise, pay some attention to<br/>style and notation. In particular, note what goes on in Sections 3.4–3.6. Such chapters<br/>are, inevitably, a compromise between wanting the book to be self-contained and not<br/>wanting to duplicate at length what is standard in other excellent references.</p><p>Chapter 4 gets you into the heart of inference issues fairly quickly. The approach to<br/>inference is semiparametric and asymptotic in nature. This leads to a statistical theory<br/>that is different from classical contexts. We assume there is some structure out there<br/>at asymptopia and we are trying to infer what it is using a pitiful finite sample whose<br/>true model has not yet converged to the asymptotic model. Thus, maximum likelihood<br/>methods are not really available unless we simply assume from some threshold onwards<br/>that the asymptotic model holds. We give some diagnostics that help decide on values<br/>of parameters and when a heavy-tail model is appropriate.<br/>Chapter 5 begins the probability treatment which is geared towards a dimensionless<br/>theory. It focuses on the Poisson process and stochastic processes derived from the<br/>Poisson process, including Lévy and extremal processes. We also give an introduction<br/>to data network modeling. Chapter 6 gives the dimensionless treatment of regular<br/>variation and its probabilistic equivalents. We survey weak convergence techniques<br/>and discuss why it is difficult to bootstrap heavy-tail phenomena. Chapter 7 exploits<br/>the weak convergence technology to discuss weak convergence of extremes to extremal<br/>processes and weak convergence of summation processes to Lévy limits. Special cases<br/>include sums of heavy-tailed iid random variables converging to α-stable Lévy motion.<br/>We close the chapter with a unit on how weak convergence techniques can be used<br/>to study various transformations of regularly varying random vectors. We include<br/>Tauberian theory for Laplace transforms in this discussion.<br/>Applied probability takes center stage in Chapter 8 which uses heavy-tail techniques<br/>to learn about the properties of three models. Two of the models are for data networks<br/>and the last one is a more traditional queueing model. We return to statistical issues in<br/>Chapter 9, discussing asymptotic normality for estimators and then moving to inference<br/>for multivariate heavy-tailed models. We include examples of analysis of exchange rate<br/>data, Internet data, telephone network data and insurance data. Finally, we close the<br/>chapter with a discussion of the much praised and vilified sample correlation function.<br/>There are some appendices devoted to notational conventions and a list of symbols and<br/>also a section which timidly discusses some useful software.<br/>Each chapter contains exercises.</p><p>识货的赶快下！</p>
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