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Statistical Inference from Stochastic Processes
Edited by: N. U. Prabhu
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Contemporary Mathematics
1988; 386 pp; softcover
Volume: 80
ISBN-10: 0-8218-5087-3
ISBN-13: 978-0-8218-5087-9
List Price: US$53
Member Price: US$42.40
Order Code: CONM/80
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This volume comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. The conference brought together probabilists and statisticians who have developed important areas of application and made major contributions to the foundations of the subject.

Statistical inference from stochastic processes has been important in a number of areas. For example, in applied probability, major advances have been made in recent years in stochastic models arising in science and engineering. However, the emphasis has been on the formulation and analysis of models rather than on the statistical methodology for hypothesis testing and inference. For these models to be of practical use, procedures for their statistical analysis are essential.

In the area of probability models, initial work in inference focused on Markov chains, but many models have given rise to non-Markovian and point processes. In recent years, research in statistical inference from such processes not only solved specific problems but also resulted in major contributions to the conceptual framework of the subject as well as the associated techniques.

The objective of the conference was to provide the opportunity to survey and evaluate the current state of the art in this area and to discuss future directions. The papers presented covered five topics within the broad domain of inference from stochastic processes: foundations, counting processes and survival analysis, likelihood and its ramifications, applications to statistics and probability models, and processes in economics. Requiring a graduate level background in probability and statistical inference, this book will provide students and researchers with a familiarity with the foundations of inference from stochastic processes and a knowledge of the current developments in this area.

Table of Contents

  • P. E. Greenwood -- Partially specified semimartingale experiments
  • P. K. Andersen, O. Borgan, R. D. Gill, and N. Keiding -- Censoring, truncation, and filtering in statistical models based on counting processes
  • M. Jacobsen -- Right censoring and the Kaplan-Meier and Nelson-Aalen estimators. Summary of results
  • D. Oakes -- Partial likelihood: applications, ramifications, generalizations
  • P. C. B. Phillips -- Multiple regression with integrated time series
  • N. M. Kiefer -- Analysis of grouped duration data
  • I. W. McKeague -- Asymptotic theory for weighted least squares estimators in Aalen's additive risk model
  • M. J. Phelan -- Some applications in statistics of semimartingale weak convergence theorems
  • Y. Ritov and J. A. Wellner -- Censoring, martingales and the Cox model
  • B. G. Lindsay -- Composite likelihood methods
  • C. C. Heyde -- Fixed sample and asymptotic optimality for classes of estimating functions
  • B. L. S. P. Rao -- Statistical inference from sampled data for stochastic processes
  • B. R. Bhat -- Optimal properties of SPRT for some stochastic processes
  • J. Winnicki -- Estimation theory for the branching process with immigration
  • V. T. Stefanov -- A sequential approach for reducing curved exponential families of stochastic processes to noncurved exponential ones
  • A. F. Karr -- Palm distributions of point processes and their applications to statistical inference
  • S. Johansen -- The mathematical structure of error correction models
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