Semimartingales and their Statistical Inference  book cover
1st Edition

Semimartingales and their Statistical Inference

ISBN 9780367399757
Published June 19, 2019 by CRC Press
450 Pages

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Book Description

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.
  • Table of Contents

    Exponential Families of Stochastic Processes
    Asymptotic Likelihood Theory
    Local Asymptotic Behavior of Semimartingales Experiments
    Likelihood and Asymptotic Efficiency
    Applications to Stochastic Modeling

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    Rao, B.L.S. Prakasa