Empirical Process Techniques for Dependent Data

Inbunden, Engelska, 2002

1 484 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Beskrivning

Empirical process techniques have been used for many years in statistics and probability theory. In the recent past, the need to model dependence in real-life data sets has led to new developments for the empirical distribution function and the empirical process for dependent, mostly stationary sequences. Some work has been motivated by the classical results for {\ it independent} data and has been aimed at deriving similar results for stationary sequences. While the theory for {\ it dependent} data is well understood, no comprehensive text exists to date on the subject. The book is divided into two parts: Part I focuses on a thorough introduction to the existing theory of empirical process techniques for dependent data, starting from the classical contributions of Billingsley to present day research. Part II provides an overview of the most recent applications in various fields related to empirical processes, e.g., spectral analysis of time series, the bootstrap for stationary sequences, and the empirical process for mixing dependent observations, including the case of strong dependence. Top specialists contributing to the volume are: S.I. Resnick, H. Drees, R.A. Davis, T.Hsing, M. Arcones, E. Rio, P. Doukhan, L. Horvath, L. Giraitis, D. Surgailis, R. Dahlhaus, P. Soulier, R.V. Sachs, H.-R. Kunsch, P. Buhlmann, M. Peligrad, H. Dehling, Philipp To date this book is the only comprehensive treatment of the topic in the literature. It will serve as a reference or resource for classroom use in the areas of statistics, time series analysis, extreme value theory, point process theory, and applied probability theory.

Produktinformation

Utgivningsdatum:2002-08-19
Mått:178 x 254 x 24 mm
Vikt:903 g
Format:Inbunden
Språk:Engelska
Antal sidor:383
Upplaga:2002
Förlag:Birkhauser Boston Inc
ISBN:9780817642013

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Recensioner i media

"The book is an outgrowth of the workshop held in November 2000 at the University of Copenhagen. It opens by an extensive tutorial covering the topic from the early roots up to recent developments and is accompanied by a vast bibliography of newly 150 items... The book is the first comprehensive treatment of this topic, perhaps because only the present-day computers are able to meet the enormous requirements for high speed and large memory necessary for the application of statistical techniques to dependent data. It will be suitable for classroom use as well as for specialists in probability and statistics and for practitioners in the above mentioned branches of dependent data applications." ---APPLICATIONS OF MATHEMATICS

Innehållsförteckning

I. A Tutorial on Empirical Process Techniques for Dependent Data.- Empirical Process Techniques for Dependent Data.- II. Techniques for the Empirical Process of Stationary Sequences.- Weak Dependence: Models and Applications.- Maximal Inequalities and Empirical Central Limit Theorems.- On Hoeffding’s Inequality for Dependent Random Variables.- On the Coupling of Dependent Random Variables and Applications.- Empirical Processes of Residuals.- III. The Empirical Process of Long Range Dependent Processes.- Asymptotic Expansion of the Empirical Process of Long Memory Moving Averages.- The Reduction Principle for the Empirical Process of a Long Memory Linear Process.- Distributional Limit Theorems for Empirical Processes Generated by Functions of a Stationary Gaussian Process.- IV. Empirical Spectral Process Techniques.- Empirical Spectral Processes and Nonparametric Maximum Likelihood Estimation for Time Series.- Empirical Processes Techniques for the Spectral Estimation of Fractional Processes.- V. The Tail Empirical Process in Extreme Value Theory.- Tail Empirical Processes Under Mixing Conditions.- VI. Bootstrap Techniques.- On the Bootstrap and Empirical Processes for Dependent Sequences.- Frequency Domain Bootstrap for Time Series.