Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

Introduction to Mathematical Statistics. By R.V. Hogg and A. T. Craig. Pp. ix, 245. 47s. 1959. (The Macmillan Company, New York)

Here are two books on a topic new to Technometrics: statistical and mathematical demography. The first author of Applied Mathematical Demography wrote the first two editions of this book alone. The second edition was published in 1985. Professor Keyfritz noted in the Preface (p. vii) that at age 90 he had no interest in doing another edition; however, the publisher encouraged him to find a coauthor. The result is an additional focus for the book in the world of biology that makes it much more relevant for the sciences. The book is now part of the publisher’s series on Statistics for Biology and Health. Much of it, of course, focuses on the many aspects of human populations. The new material focuses on mature population models, the particular focus of the new author (see, e.g., Caswell 2000). As one might expect from a book that was originally written in the 1970s, it does not include a lot of information on statistical computing. The new book by Alho and Spencer is focused on putting a better emphasis on statistics in the discipline of demography (Preface, p. vii). It is part of the publisher’s Series in Statistics. The authors are both statisticians, so the focus is on statistics as used for demographic problems. The authors are targeting human applications, so their perspective on science does not extend any further than epidemiology. The book actually strikes a good balance between statistical tools and demographic applications. The authors use the first two chapters to teach statisticians about the concepts of demography. The next four chapters are very similar to the statistics content found in introductory books on survival analysis, such as the recent book by Kleinbaum and Klein (2005), reported by Ziegel (2006). The next three chapters are focused on various aspects of forecasting demographic rates. The book concludes with chapters focusing on three areas of applications: errors in census numbers, financial applications, and small-area estimates.

Univariate Discrete Distributions

of the conditional distribution speci cations. Chapters 8 and 10 extend these methods from two to more dimensions. Chapter 9 investigates estimation in conditionally speci ed models. Chapter 11 considers models speci ed by conditioning on events speci ed by one variable exceeding a value rather than equaling a value, and Chapter 12 considers models for extreme-value data. Chapter 13 extends conditional speci cation to Bayesian analysis. Chapter 14 describes the related simultaneous-equation models, and Chapter 15 ties in some additional topics. An appendix describes methods of simulation from conditionally speci ed models. Chapters 1–4, plus Chapters 9 and 13, comprise a lively overview of conditionally speci ed models. The remainder of the text constitutes a detailed catalog of results speci c to different conditional distributions. Although this catalog is certainly of value, the reader desiring a briefer and less detailed introduction to the subject might skip the remainder at  rst reading. This text is a revision of the book by Arnold, Costillo, and Sarabia (1992). The current version is of similar breadth, but with much more depth than the original. The text is clearly written and accessible with relatively few mathematical prerequisites. I found surprisingly few typographical errors; the authors are to be congratulated for this. In a few cases, regularity conditions for results are not given in full. Generally, this causes little confusion, although something does appear to be missing in the statement of Aczél’s key theorem (Theorem 1.3). Fortunately, most of the results in the sequel are derived from corollaries to this theorem, and the corollaries are stated more precisely. I noted few gaps in the material covered. The only area that I thought was insuf ciently represented was application to Markov chain Monte Carlo. Conditional speci cation is particularly important in Gibbs sampling. I believe that many practitioners would bene t from a discussion of the issues involved in these sampling schemes. Each chapter contains numerous exercises. These exercises appear to be at an appropriate level for a graduate course in statistics, and appear to provide appropriate reinforcement for the material in the preceding chapters.

Runs and Scans With Applications

In this article, we propose the fractional lower order covariance method (FLOC) for estimating the parameters of vector autoregressive process (VAR) of order $p$, $p\geq 1$ with symmetric stable noise. Further, we show the efficiency, accuracy, and simplicity of our methods through Monte-Carlo simulation.

Estimation of the Parameters of Vector Autoregressive (VAR) Time Series Model with Symmetric Stable Noise

In this work, we analyze the maximum number of wireless transmitters (nodes) that can be scheduled subject to interference constraints across the nodes. Given a set of nodes, the problem reduces to finding the maximum cardinality of a subset that can concurrently transmit without violating interference constraints. The resulting packing problem is a binary optimization problem, which is NP hard. We propose a semi-definite (SDP) relaxation for the NP hard problem and discuss the algorithm and the quality of the relaxation by providing approximation ratios for the relaxation.

Maximal Packing with Interference Constraints

For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model. Usually, dynamic programming techniques are applied to optimize the portfolio for the multi-period model. However, this assumes a known distribution for the parameters of the financial time series. We consider the situation where the distribution of parameters is unknown and is estimated directly from the dynamically arriving data. We implement the Bayesian filtering method through dynamic linear models to sequentially update the parameters. We also acknowledge the uncertain investment lifetime to make the model more adaptive to the market conditions. These updated parameters are put into the dynamic mean–variance problem to arrive at optimal efficient portfolios. Implementing this model to the S&P500 illustrates that the data strongly favor the Bayesian updating and is practically implementable.

Bayesian Filtering for Multi-period Mean–Variance Portfolio Selection

In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical characteristic function method for the estimation of GARCH parameters with symmetric stable noise. Further, we show the efficiency, accuracy, and simplicity of our methods through Monte-Carlo simulation. Finally, we apply our proposed methods to model financial data.

N. S. Upadhye

Papers

Estimation of the Parameters of Vector Autoregressive (VAR) Time Series Model with Symmetric Stable Noise

Maximal Packing with Interference Constraints

Bayesian Filtering for Multi-period Mean–Variance Portfolio Selection

Estimation of the Parameters of Symmetric Stable ARMA and ARMA-GARCH Models

On first-come, first-served queues with three classes of impatient customers