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Author: Constance van Eeden
Publisher: Springer Science & Business Media
ISBN: 038748809X
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This monograph is addressed to anyone interested in the subject of restrict- parameter-space estimation, and in particular to those who want to learn, or bring their knowledge up to date, about (in)admissibility and minimaxity problems for such parameter spaces. The coverage starts in the early 1950s when the subject of inference for - stricted parameter spaces began to be studied and ends around the middle of 2004. It presents known, and also some new, results on (in)admissibility and minimaxity for nonsequential point estimation problems in restricted ?ni- dimensional parameter spaces. Relationships between various results are d- cussed and open problems are pointed out. Few complete proofs are given, but outlines of proofs are often supplied. The reader is always referred to the published papers and often results are clari?ed by presenting examples of the kind of problems an author solves, or of problems that cannot be solved by a particular result. The monograph does not touch on the subject of testing hypotheses in - stricted parameter spaces. The latest books on that subject are by Robertson, Wright and Dykstra (1988) and Akkerboom (1990), but many new results in that area have been obtained since. The monograph does have a chapter in which questions about the existence of maximum likelihood estimators are discussed. Some of their properties are also given there as well as some algorithms for computing them. Most of these results cannot be found in the Robertson, Wright, Dykstra book.
Author: Constance van Eeden
Publisher: Springer Science & Business Media
ISBN: 038748809X
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
This monograph is addressed to anyone interested in the subject of restrict- parameter-space estimation, and in particular to those who want to learn, or bring their knowledge up to date, about (in)admissibility and minimaxity problems for such parameter spaces. The coverage starts in the early 1950s when the subject of inference for - stricted parameter spaces began to be studied and ends around the middle of 2004. It presents known, and also some new, results on (in)admissibility and minimaxity for nonsequential point estimation problems in restricted ?ni- dimensional parameter spaces. Relationships between various results are d- cussed and open problems are pointed out. Few complete proofs are given, but outlines of proofs are often supplied. The reader is always referred to the published papers and often results are clari?ed by presenting examples of the kind of problems an author solves, or of problems that cannot be solved by a particular result. The monograph does not touch on the subject of testing hypotheses in - stricted parameter spaces. The latest books on that subject are by Robertson, Wright and Dykstra (1988) and Akkerboom (1990), but many new results in that area have been obtained since. The monograph does have a chapter in which questions about the existence of maximum likelihood estimators are discussed. Some of their properties are also given there as well as some algorithms for computing them. Most of these results cannot be found in the Robertson, Wright, Dykstra book.
Author: Bernard Fichet
Publisher: Springer Science & Business Media
ISBN: 3642133126
Category : Mathematics
Languages : en
Pages : 460
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Book Description
The growing capabilities in generating and collecting data has risen an urgent need of new techniques and tools in order to analyze, classify and summarize statistical information, as well as to discover and characterize trends, and to automatically bag anomalies. This volume provides the latest advances in data analysis methods for multidimensional data which can present a complex structure: The book offers a selection of papers presented at the first Joint Meeting of the Société Francophone de Classification and the Classification and Data Analysis Group of the Italian Statistical Society. Special attention is paid to new methodological contributions from both the theoretical and the applicative point of views, in the fields of Clustering, Classification, Time Series Analysis, Multidimensional Data Analysis, Knowledge Discovery from Large Datasets, Spatial Statistics.
Author: Phoebus J. Dhrymes
Publisher: Springer Science & Business Media
ISBN: 1461243025
Category : Business & Economics
Languages : en
Pages : 411
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Book Description
This book is intended for second year graduate students and professionals who have an interest in linear and nonlinear simultaneous equations mod els. It basically traces the evolution of econometrics beyond the general linear model (GLM), beginning with the general linear structural econo metric model (GLSEM) and ending with the generalized method of mo ments (GMM). Thus, it covers the identification problem (Chapter 3), maximum likelihood (ML) methods (Chapters 3 and 4), two and three stage least squares (2SLS, 3SLS) (Chapters 1 and 2), the general nonlinear model (GNLM) (Chapter 5), the general nonlinear simultaneous equations model (GNLSEM), the special ca'3e of GNLSEM with additive errors, non linear two and three stage least squares (NL2SLS, NL3SLS), the GMM for GNLSEIVl, and finally ends with a brief overview of causality and re lated issues, (Chapter 6). There is no discussion either of limited dependent variables, or of unit root related topics. It also contains a number of significant innovations. In a departure from the custom of the literature, identification and consistency for nonlinear models is handled through the Kullback information apparatus, as well as the theory of minimum contrast (MC) estimators. In fact, nearly all estimation problems handled in this volume can be approached through the theory of MC estimators. The power of this approach is demonstrated in Chapter 5, where the entire set of identification requirements for the GLSEM, in an ML context, is obtained almost effortlessly, through the apparatus of Kullback information.
Author: David Dunson
Publisher: Springer Science & Business Media
ISBN: 0387767215
Category : Mathematics
Languages : en
Pages : 174
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Book Description
Random Effect and Latent Variable Model Selection In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of ?elds. For example, it is now standard pr- tice to routinely collect many response variables on each individual in a study. The different variables may correspond to repeated measurements over time, to a battery of surrogates for one or more latent traits, or to multiple types of outcomes having an unknown dependence structure. Hierarchical models that incorporate subje- speci?c parameters are one of the most widely-used tools for analyzing multivariate and correlated data. Such subject-speci?c parameters are commonly referred to as random effects, latent variables or frailties. There are two modeling frameworks that have been particularly widely used as hierarchical generalizations of linear regression models. The ?rst is the linear mixed effects model (Laird and Ware , 1982) and the second is the structural equation model (Bollen , 1989). Linear mixed effects (LME) models extend linear regr- sion to incorporate two components, with the ?rst corresponding to ?xed effects describing the impact of predictors on the mean and the second to random effects characterizing the impact on the covariance. LMEs have also been increasingly used for function estimation. In implementing LME analyses, model selection problems are unavoidable. For example, there may be interest in comparing models with and without a predictor in the ?xed and/or random effects component.
Author: Jérome Dedecker
Publisher: Springer Science & Business Media
ISBN: 038769952X
Category : Mathematics
Languages : en
Pages : 326
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Book Description
This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.
Author: Piotr Jaworski
Publisher: Springer Science & Business Media
ISBN: 3642124658
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
Author: Christoph Koenig
Publisher: Frontiers Media SA
ISBN: 2889742148
Category : Science
Languages : en
Pages : 197
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Book Description
Author: Pavel S. Knopov
Publisher: Springer Science & Business Media
ISBN: 1461405742
Category : Business & Economics
Languages : en
Pages : 245
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Book Description
This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance
Author: Lang Wu
Publisher: CRC Press
ISBN: 9781420074086
Category : Mathematics
Languages : en
Pages : 431
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Book Description
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Author: Malay Ghosh
Publisher: Routledge
ISBN: 1351464426
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Assuming a basic knowledge of the frequentist approach to finite population sampling, Bayesian Methods for Finite Population Sampling describes Bayesian and predictive approaches to inferential problems with an emphasis on the likelihood principle. The authors demonstrate that a variety of levels of prior information can be used in survey sampling in a Bayesian manner. Situations considered range from a noninformative Bayesian justification of standard frequentist methods when the only prior information available is the belief in the exchangeability of the units to a full-fledged Bayesian model. Intended primarily for graduate students and researchers in finite population sampling, this book will also be of interest to statisticians who use sampling and lecturers and researchers in general statistics and biostatistics.
