Asymptotic Statistics


Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 9780521784504
Category: Mathematics
Page: 443
View: 9848

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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: 5117

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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: 7125

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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: 6917

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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: 4273

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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.

Kalman-Bucy-Filter

determinist. Beobachtung u. stochast. Filterung
Author: Karl Brammer,Gerhard Siffling
Publisher: N.A
ISBN: N.A
Category: Control theory
Page: 232
View: 6262

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Das Buch will die mannigfaltigen Aufgaben der heutigen Regelungs- und Steuerungstechnik und ihre Lösung nahebringen. Das soll mit möglichst geringem Zeit- und Arbeitsaufwand für den Leser verbunden sein. Leichte Verständlichkeit, Anschaulichkeit und Anwendungsnähe sind deshalb Hauptgesichtspunkt der Darstellung. Vollständigkeit ist nicht angestrebt, vielmehr Darstellung des Wesentlichen. Mathematische Methoden werden auf das Notwendige beschränkt.

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: 4703

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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.

Wahrscheinlichkeitsrechnung und Statistik


Author: Robert Hafner
Publisher: Springer-Verlag
ISBN: 3709169445
Category: Mathematics
Page: 512
View: 9388

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Das Buch ist eine Einführung in die Wahrscheinlichkeitsrechnung und mathematische Statistik auf mittlerem mathematischen Niveau. Die Pädagogik der Darstellung unterscheidet sich in wesentlichen Teilen – Einführung der Modelle für unabhängige und abhängige Experimente, Darstellung des Suffizienzbegriffes, Ausführung des Zusammenhanges zwischen Testtheorie und Theorie der Bereichschätzung, allgemeine Diskussion der Modellentwicklung – erheblich von der anderer vergleichbarer Lehrbücher. Die Darstellung ist, soweit auf diesem Niveau möglich, mathematisch exakt, verzichtet aber bewußt und ebenfalls im Gegensatz zu vergleichbaren Texten auf die Erörterung von Meßbarkeitsfragen. Der Leser wird dadurch erheblich entlastet, ohne daß wesentliche Substanz verlorengeht. Das Buch will allen, die an der Anwendung der Statistik auf solider Grundlage interessiert sind, eine Einführung bieten, und richtet sich an Studierende und Dozenten aller Studienrichtungen, für die mathematische Statistik ein Werkzeug ist.

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: 7045

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

On Goodness-of-fit Tests of Semiparametric Models


Author: Bo Li
Publisher: N.A
ISBN: N.A
Category:
Page: 266
View: 7769

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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.

Statistical Models


Author: A. C. Davison
Publisher: Cambridge University Press
ISBN: 1139437410
Category: Mathematics
Page: N.A
View: 5937

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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.

High-Dimensional Statistics

A Non-Asymptotic Viewpoint
Author: Martin J. Wainwright
Publisher: Cambridge University Press
ISBN: 1108498027
Category: Business & Economics
Page: 555
View: 9793

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A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Statistik II für Dummies


Author: Deborah J. Rumsey
Publisher: John Wiley & Sons
ISBN: 3527669248
Category: Mathematics
Page: 372
View: 2769

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Vom Absolutrang bis zum Zweifach-Varianzanalysemodell – alles, was Sie über weiterführende Statistik wissen sollten Es gibt Qualen, große Qualen und Statistik, so sehen es viele Studenten. Mit diesem Buch lernen Sie weiterführende Statistik so leicht wie möglich. Deborah Rumsey zeigt Ihnen, wie Sie Varianzanalysen und Chi-Quadrat-Tests berechnen, wie Sie mit Regressionen arbeiten, ein Modell erstellen, Korrelationen bilden, nichtparametrische Prozeduren durchführen und vieles mehr. Aber auch die Grundlagen der Statistik bleiben nicht außen vor und deshalb erklärt Ihnen die Autorin, was Sie zu Mittelwerten, Vertrauensintervallen und Co wissen sollten. So lernen Sie die Methoden, die Sie brauchen, und erhalten das Handwerkszeug, um erfolgreich Ihre Statistikprüfungen zu bestehen. Sie erfahren: • Wie Sie mit multiplen Regressionen umgehen • Was es mit dem Vorzeichentest und dem Vorzeichenrangtest auf sich hat • Wie Sie sich innerhalb der statistischen Techniken zurechtfinden • Was das richtige Regressionsmodell für Ihre Analyse ist • Wie Regression und ANOVA zusammenhängen

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: 2430

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