Semimartingales and Their Statistical Inference

Semimartingales and Their Statistical Inference

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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.show more

Product details

  • Hardback | 450 pages
  • 156 x 226 x 40mm | 961.62g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • notes, references
  • 1584880082
  • 9781584880080
  • 1,863,601

Review quote

"This is a book for experienced statisticians and modellers and it is certainly to be recommended for libraries." --C. C. Heyde, Australian National University, Canberra,show more

Table of contents

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 Inference for Counting Processes Inference for Additive-Multiplicative Hazard Models Inference for Semimartingale Regression Models Estimation by the Quasi-Least-Squares Method Estimation by the Maximum Likelihood Method Estimation by the Method of Sieves Nonlinear Semimartingale Regression Models Applications to Stochastic Modeling Introduction Applications to Engineering and Economic Systems Applications to Modeling of Neuron Movement in Nervous Systems Appendix Doleans Measure for Semimartingales and Burkholder's Inequality for Martingales Interchanging Stochastic Integration and Ordinary Differentiation and Fubini-Type Theorem for Stochastic Integrals The Fundamental Identity of the Sequential Analysis Stieltjes-Lebesgue Calculus A Useful Lemma Contiguity Notes Referencesshow more