Semimartingales and their Statistical Inference

 
 
Routledge (Verlag)
  • erschienen am 15. Januar 2019
  • |
  • 450 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-1-351-41692-4 (ISBN)
 
Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability.
The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales.

Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include:

  • Asymptotic likelihood theory
  • Quasi-likelihood
  • Likelihood and efficiency
  • Inference for counting processes
  • Inference for semimartingale regression models

    The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.
  • Englisch
  • London
  • |
  • Großbritannien
Taylor & Francis Ltd
  • Für höhere Schule und Studium
  • 7,33 MB
978-1-351-41692-4 (9781351416924)
Semimartingales
Introduction
Stochastic Processes
Doob-Meyer Decomposition
Stochastic Integration
Local Martingales
Semimartingales
Girsanov's Theorem
Limit Theorems for Semimartingales
Diffusion Type Processes
Point Processes
Exponential Families of Stochastic Processes
Introduction
Exponential Families of Semimartingales
Stochastic Time Transformation
Asymptotic Likelihood Theory
Introduction
Examples
Asymptotic Likelihood Theory for a Class of Exponential Families of Semimartingales
Asymptotic Likelihood Theory for General Processes
Exercises
Asymptotic Likelihood Theory for Diffusion Processes with Jumps
Introduction
Absolute Continuity for Measures Generated by Diffusions with Jumps
Score Vector and Information Matrix
Asymptotic Likelihood Theory for Diffusion Processes with Jumps
Asymptotic Likelihood Theory for Exponential Families
Examples
Exercises
Quasi-likelihood and Semimartingales
Quasi-Likelihood and Discrete Time Processes
Quasi-Likelihood and Continuous Time Processes
Quasi-Likelihood and Special Semimartingales
Quasi-Likelihood and Partially Specified Counting Processes
Examples
Exercises
Local Asymptotic Behavior of Semimartingales Experiments
Locally Asymptotic Mixed Normality
Locally Asymptotic Quadraticity
Locally Asymptotic Infinite Divisibility
Locally Asymptotic Normality (Infinite Dimensional Parameter Case)
Multiplicative Models and Asymptotic Variance Bounds
Exercises
Likelihood and Asymptotic Efficiency
Fully Specified Likelihood (Factorisable Models)
Partially Specified Likelihood
Partial Likelihood and Asymptotic Efficiency
Partially Specified Likelihood and Asymptotic Efficiency
Inference for Counting Processes
Introduction
Parametric Inference for Counting Processes
Semiparametric Inference for Counting Processes
Nonparametric In

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