Asymptotic Statistics


Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 9780521784504
Category: Mathematics
Page: 443
View: 3069

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A mathematically rigorous, practical introduction presenting standard topics plus research.

Advances in Directional and Linear Statistics

A Festschrift for Sreenivasa Rao Jammalamadaka
Author: Martin T. Wells,Ashis SenGupta
Publisher: Springer Science & Business Media
ISBN: 9783790826289
Category: Mathematics
Page: 321
View: 7081

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The present volume consists of papers written by students, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from various countries, and covers a variety of research topics which he enjoys and contributed immensely to.

Statistical Inference for Financial Engineering


Author: Masanobu Taniguchi,Tomoyuki Amano,Hiroaki Ogata,Hiroyuki Taniai
Publisher: Springer Science & Business Media
ISBN: 3319034979
Category: Business & Economics
Page: 118
View: 993

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​This monograph provides the fundamentals of statistical inference for financial engineering and covers some selected methods suitable for analyzing financial time series data. In order to describe the actual financial data, various stochastic processes, e.g. non-Gaussian linear processes, non-linear processes, long-memory processes, locally stationary processes etc. are introduced and their optimal estimation is considered as well. This book also includes several statistical approaches, e.g., discriminant analysis, the empirical likelihood method, control variate method, quantile regression, realized volatility etc., which have been recently developed and are considered to be powerful tools for analyzing the financial data, establishing a new bridge between time series and financial engineering. This book is well suited as a professional reference book on finance, statistics and statistical financial engineering. Readers are expected to have an undergraduate-level knowledge of statistics.

Algebraic Statistics


Author: Seth Sullivant
Publisher: American Mathematical Soc.
ISBN: 1470435179
Category: Geometry, Algebraic
Page: 490
View: 8313

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Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Lévy Matters IV

Estimation for Discretely Observed Lévy Processes
Author: Denis Belomestny,Fabienne Comte,Valentine Genon-Catalot,Hiroki Masuda,Markus Reiß
Publisher: Springer
ISBN: 3319123734
Category: Mathematics
Page: 286
View: 3329

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The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the estimation of discretely observed Lévy processes, when the observation scheme is regular, from an up-to-date viewpoint.

From Finite Sample to Asymptotic Methods in Statistics


Author: Pranab K. Sen,Julio M. Singer,Antonio C. Pedroso de Lima
Publisher: Cambridge University Press
ISBN: 0521877229
Category: Mathematics
Page: 386
View: 604

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A broad view of exact statistical inference and the development of asymptotic statistical inference.

Statistical Models


Author: A. C. Davison
Publisher: Cambridge University Press
ISBN: 1139437410
Category: Mathematics
Page: N.A
View: 8822

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Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Applied Asymptotics

Case Studies in Small-Sample Statistics
Author: A. R. Brazzale,A. C. Davison,N. Reid
Publisher: Cambridge University Press
ISBN: 1139463837
Category: Mathematics
Page: N.A
View: 1909

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In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.

Empirical Processes in M-Estimation


Author: Sara A. van de Geer,Sara van de Geer
Publisher: Cambridge University Press
ISBN: 9780521650021
Category: Mathematics
Page: 286
View: 5813

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Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.

On Goodness-of-fit Tests of Semiparametric Models


Author: Bo Li
Publisher: N.A
ISBN: N.A
Category:
Page: 266
View: 9377

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Comprehensive model adequacy checking procedures are discussed for general parametric and semiparametric model specifications, with illustration in a variety of examples containing assumptions on dependence structures, density shapes, functional forms and other model features. We use the efficient score processes developed by Bickel, Ritov and Stoker (2006) as building blocks, from which many omnibus tests can be constructed. This set of omnibus tests include Class I tests with decreasing power along high frequencies, and Class II tests with approximately equal power on limited frequencies. We also give a unified view of a group of asymptotically distribution free tests from the score perspective. This set of tests is essentially derived from a family of inefficient scores, enabling the limit Gaussian processes to have nice variance-covariance structure. Additionally, we propose data-driven tests in the score and spectral domains. Either model selection rules or thresholding methods are invoked to choose the scores or spectra on which to focus. Finally, we consider aggregating different types of tests, primarily combining one Class I test and one Class II test, in the hope of achieving a balance between the two classes. Numerical experiments confirm that both Class I and Class II tests have their own strong and weak aspects, and the aggregated procedures demonstrate a balanced and stable performance; although signal strength (of departures) is a fundamental limiting factor of all such procedures. In summary, a statistical model is warranted only when it passes various diagnostic checks with different but complementary strengths.

Elements of Distribution Theory


Author: Thomas A. Severini
Publisher: Cambridge University Press
ISBN: 9780521844727
Category: Business & Economics
Page: 515
View: 4684

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This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Regression for Categorical Data


Author: Gerhard Tutz
Publisher: Cambridge University Press
ISBN: 1139499580
Category: Mathematics
Page: N.A
View: 943

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This book introduces basic and advanced concepts of categorical regression with a focus on the structuring constituents of regression, including regularization techniques to structure predictors. In addition to standard methods such as the logit and probit model and extensions to multivariate settings, the author presents more recent developments in flexible and high-dimensional regression, which allow weakening of assumptions on the structuring of the predictor and yield fits that are closer to the data. A generalized linear model is used as a unifying framework whenever possible in particular parametric models that are treated within this framework. Many topics not normally included in books on categorical data analysis are treated here, such as nonparametric regression; selection of predictors by regularized estimation procedures; ternative models like the hurdle model and zero-inflated regression models for count data; and non-standard tree-based ensemble methods. The book is accompanied by an R package that contains data sets and code for all the examples.

Saddlepoint Approximations with Applications


Author: Ronald W. Butler
Publisher: Cambridge University Press
ISBN: 1139466518
Category: Mathematics
Page: N.A
View: 9409

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Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

Fundamentals of Nonparametric Bayesian Inference


Author: Subhashis Ghosal,Aad van der Vaart
Publisher: Cambridge University Press
ISBN: 0521878268
Category: Business & Economics
Page: 670
View: 4568

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Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.