Bücher der Reihe Lecture Notes in Statistics

The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort.

This monograph treats the question of determining how much to spend for the collection and analysis of public data. Of course it is too late to change the 1970 census program, but the method and techniques of analysis will apply to future data programs.

The theory and practice of decision making involves infinite or finite number of actions. In this work, we have applied general decision theory to develop some modified principles which are reasonable for problems in this field.

Chapter 2 deals with discrete time theory. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech nical details. Chapter 3 deals with continuous time theory. Three applications of the continuous time theory are given in Chapter 4.

However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases.

The increasing power and decreasing price of smalI computers, especialIy "personal" computers, has made them increasingly popular in statistical analysis. The day may not be too far off when every statistician has on his or her desktop computing power on a par with the large mainframe computers of 15 or 20 years ago.

IV CONTENTS CHAPTER 1 INTRODUCTION 1. 1 Introduction 1 Appendix 1. 2 14 CHAPTER 2 STATIONARITY AND STABILITY 15 2. 1 Introduction 15 2. 2 Singly-Infinite Stationarity 16 2. 3 Doubly-Infinite Stationarity 19 2. 5 Stability of RCA Models 33 2. 6 Strict Stationarity 37 Appendix 2. 1 38 CHAPTER 3 LEAST SQUARES ESTIMATION OF SCALAR MODELS 40 3.

Since also this process theory is virtually inaccessible to non-probabilists, it would appear useful to have an account of what Aalen has done, that includes exactly the amount of probability required to deal satisfactorily and rigorously with statistical models for counting processes.

This volume of Lecture Notes in Statistics consists of the published proceedings of the first international conference to be held on the topic of generalised linear models.

Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity.

Probabilistic models of technical systems are studied here whose finite state space is partitioned into two or more subsets. The systems considered are such that each of those subsets of the state space will correspond to a certain performance level of the system.

Held in the Physikzentrum in Bad Honnef from 3-7 May, 1982

a small conference on order restricted inference was held at the University of Iowa in Iowa City in April of 1981. There were thirty-five participants and twenty presentations on a wide variety of topics dealing with order restricted inference at the second conference.

When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given.

The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.Concerning the proofs of the limit theorems, the "Fourth Moment Theorem" is systematically used, as it produces rapid and helpful proofs that can serve as models for the future.

Two themes are treated which are closely related to each other and to the law of the iterated logarithm:* I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries.

My interest in majorization was first spurred by Ingram aIkin's proclivity for finding Schur convex functions lurking in the problem section of every issue of the American Mathematical Monthly. The inequality principles of Dalton, especially the transfer or Robin Hood principle, are given appropriate prominence.

This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations.

This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications.

In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently.The test statistics in question range from common ones, such as those used to test e.g.

This book provides a unified introduction to a variety of computational algorithms for Bayesian and likelihood inference. In this third edition, I have attempted to expand the treatment of many of the techniques discussed. I have added some new examples, as well as included recent results. Exercises have been added at the end of each chapter. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), some exposure to statistical models as found in McCullagh and NeIder (1989), and for Section 6. 6 some experience with condi- tional inference at the level of Cox and Snell (1989). I have chosen not to present proofs of convergence or rates of convergence for the Metropolis algorithm or the Gibbs sampler since these may require substantial background in Markov chain theory that is beyond the scope of this book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the past ten years. I have attempted to identify key references-though due to the volatility of the field some work may have been missed.

This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.