Semimartingales and their Statistical Inference: 1st Edition (Hardback) book cover

Semimartingales and their Statistical Inference

1st Edition

By B.L.S. Prakasa Rao

CRC Press

450 pages

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Hardback: 9781584880080
pub: 1999-05-11
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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.

  • Reviews

    "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,

    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

    References

    About the Series

    Chapman & Hall/CRC Monographs on Statistics and Applied Probability

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT029000
    MATHEMATICS / Probability & Statistics / General
    MAT029010
    MATHEMATICS / Probability & Statistics / Bayesian Analysis