Author: J. Pfanzagl
Publisher: Springer Science & Business Media
ISBN: 1461257697
Category : Mathematics
Languages : en
Pages : 324
Book Description
Contributions to a General Asymptotic Statistical Theory
Author: J. Pfanzagl
Publisher: Springer Science & Business Media
ISBN: 1461257697
Category : Mathematics
Languages : en
Pages : 324
Book Description
Publisher: Springer Science & Business Media
ISBN: 1461257697
Category : Mathematics
Languages : en
Pages : 324
Book Description
Contributions to a General Asymptotic Statistical Theory
Author: W. Wefelmeyer
Publisher:
ISBN: 9781461257707
Category :
Languages : en
Pages : 328
Book Description
Publisher:
ISBN: 9781461257707
Category :
Languages : en
Pages : 328
Book Description
Asymptotic Expansions for General Statistical Models
Author: Johann Pfanzagl
Publisher: Springer Science & Business Media
ISBN: 1461564794
Category : Mathematics
Languages : en
Pages : 515
Book Description
0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.
Publisher: Springer Science & Business Media
ISBN: 1461564794
Category : Mathematics
Languages : en
Pages : 515
Book Description
0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.
Asymptotics in Statistics
Author: Lucien Le Cam
Publisher: Springer Science & Business Media
ISBN: 1461211662
Category : Mathematics
Languages : en
Pages : 299
Book Description
This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.
Publisher: Springer Science & Business Media
ISBN: 1461211662
Category : Mathematics
Languages : en
Pages : 299
Book Description
This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.
Asymptotic Statistics
Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 1107268443
Category : Mathematics
Languages : en
Pages :
Book Description
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
Publisher: Cambridge University Press
ISBN: 1107268443
Category : Mathematics
Languages : en
Pages :
Book Description
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
Stochastic Visibility in Random Fields
Author: Shelemyahu Zacks
Publisher: Springer
ISBN: 1461226902
Category : Mathematics
Languages : en
Pages : 188
Book Description
The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.
Publisher: Springer
ISBN: 1461226902
Category : Mathematics
Languages : en
Pages : 188
Book Description
The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.
Random Sums and Branching Stochastic Processes
Author: Ibrahim Rahimov
Publisher: Springer Science & Business Media
ISBN: 9780387944463
Category : Mathematics
Languages : en
Pages : 212
Book Description
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Publisher: Springer Science & Business Media
ISBN: 9780387944463
Category : Mathematics
Languages : en
Pages : 212
Book Description
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Classification and Dissimilarity Analysis
Author: Bernard van Cutsem
Publisher: Springer Science & Business Media
ISBN: 1461226864
Category : Mathematics
Languages : en
Pages : 251
Book Description
Classifying objects according to their likeness seems to have been a step in the human process of acquiring knowledge, and it is certainly a basic part of many of the sciences. Historically, the scientific process has involved classification and organization particularly in sciences such as botany, geology, astronomy, and linguistics. In a modern context, we may view classification as deriving a hierarchical clustering of objects. Thus, classification is close to factorial analysis methods and to multi-dimensional scaling methods. It provides a mathematical underpinning to the analysis of dissimilarities between objects.
Publisher: Springer Science & Business Media
ISBN: 1461226864
Category : Mathematics
Languages : en
Pages : 251
Book Description
Classifying objects according to their likeness seems to have been a step in the human process of acquiring knowledge, and it is certainly a basic part of many of the sciences. Historically, the scientific process has involved classification and organization particularly in sciences such as botany, geology, astronomy, and linguistics. In a modern context, we may view classification as deriving a hierarchical clustering of objects. Thus, classification is close to factorial analysis methods and to multi-dimensional scaling methods. It provides a mathematical underpinning to the analysis of dissimilarities between objects.
Maximum Likelihood Estimation of Functional Relationships
Author: Nico J.D. Nagelkerke
Publisher: Springer Science & Business Media
ISBN: 1461228581
Category : Mathematics
Languages : en
Pages : 118
Book Description
The theory of functional relationships concerns itself with inference from models with a more complex error structure than those existing in regression models. We are familiar with the bivariate linear relationship having measurement errors in both variables and the fact that the standard regression estimator of the slope underestimates the true slope. One complication with inference about parameters in functional relationships, is that many of the standard properties of likelihood theory do not apply, at least not in the form in which they apply to e.g. regression models. This is probably one of the reasons why these models are not adequately discussed in most general books on statistics, despite their wide applicability. In this monograph we will explore the properties of likelihood methods in the context of functional relationship models. Full and conditional likelihood methods are both considered. Possible modifications to these methods are considered when necessary. Apart from exloring the theory itself, emphasis shall be placed upon the derivation of useful estimators and their second moment properties. No attempt is made to be mathematically rigid. Proofs are usually outlined with extensive use of the Landau 0(.) and 0(.) notations. It is hoped that this shall provide more insight than the inevitably lengthy proofs meeting strict standards of mathematical rigour.
Publisher: Springer Science & Business Media
ISBN: 1461228581
Category : Mathematics
Languages : en
Pages : 118
Book Description
The theory of functional relationships concerns itself with inference from models with a more complex error structure than those existing in regression models. We are familiar with the bivariate linear relationship having measurement errors in both variables and the fact that the standard regression estimator of the slope underestimates the true slope. One complication with inference about parameters in functional relationships, is that many of the standard properties of likelihood theory do not apply, at least not in the form in which they apply to e.g. regression models. This is probably one of the reasons why these models are not adequately discussed in most general books on statistics, despite their wide applicability. In this monograph we will explore the properties of likelihood methods in the context of functional relationship models. Full and conditional likelihood methods are both considered. Possible modifications to these methods are considered when necessary. Apart from exloring the theory itself, emphasis shall be placed upon the derivation of useful estimators and their second moment properties. No attempt is made to be mathematically rigid. Proofs are usually outlined with extensive use of the Landau 0(.) and 0(.) notations. It is hoped that this shall provide more insight than the inevitably lengthy proofs meeting strict standards of mathematical rigour.
Contributions to Stochastics
Author: Sendler
Publisher: Springer Science & Business Media
ISBN: 3642468934
Category : Mathematics
Languages : en
Pages : 265
Book Description
Since the contributions to this volume stem from very different fields, no attempt was made to find a systematic ordering. All results are new in so far as they have not been published so far.
Publisher: Springer Science & Business Media
ISBN: 3642468934
Category : Mathematics
Languages : en
Pages : 265
Book Description
Since the contributions to this volume stem from very different fields, no attempt was made to find a systematic ordering. All results are new in so far as they have not been published so far.