Combinatorial Methods In Density Estimation

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Combinatorial Methods In Density Estimation

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Author : Luc Devroye
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Combinatorial Methods In Density Estimation written by Luc Devroye and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

Combinatorial Methods In Density Estimation

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Author : Luc Devroye
language : en
Publisher: Springer
Release Date : 2011-04-26

Combinatorial Methods In Density Estimation written by Luc Devroye and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-26 with categories.

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Nonparametric Kernel Density Estimation And Its Computational Aspects

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Author : Artur Gramacki
language : en
Publisher: Springer
Release Date : 2017-12-21

Nonparametric Kernel Density Estimation And Its Computational Aspects written by Artur Gramacki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Technology & Engineering categories.

This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.

Models For Discrete Longitudinal Data

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Author : Geert Molenberghs
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-30

Models For Discrete Longitudinal Data written by Geert Molenberghs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-30 with Mathematics categories.

The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.

Introduction To Rare Event Simulation

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Author : James Bucklew
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Introduction To Rare Event Simulation written by James Bucklew and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

This book is an attempt to present a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. This framework allows us to view a vast assortment of simulation problems from a single unified perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Unfortunately, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. In this text, I have tried to keep the mathematical preliminaries to a minimum; the only prerequisite is a single large deviation theorem dealing with sequences of Rd valued random variables. (This theorem and a proof are given in the text.) Large deviation theory is a burgeoning area of probability theory and many of the results in it can be applied to simulation problems. Rather than try to be as complete as possible in the exposition of all possible aspects of the available theory, I have tried to concentrate on demonstrating the methodology and the principal ideas in a fairly simple setting. Madison, Wisconsin 2003 James Antonio Bucklew Contents 1. Random Number Generation . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1.1 Uniform Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Nonuniform Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 The Inversion Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 The Acceptance---Rejection Method . . . . . . . . . . . . 10 . . . . . 1.3 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . 13 . . . . . . . . . . . 1.3.1 Inversion by Truncation of a ContinuousAnalog. . . . . . 14 1.3.2 Acceptance---Rejection . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . .

Nonparametric And Semiparametric Models

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Author : Wolfgang Karl Härdle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-27

Nonparametric And Semiparametric Models written by Wolfgang Karl Härdle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Mathematics categories.

The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

Reliability Life Testing And The Prediction Of Service Lives

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Author : Sam C. Saunders
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-26

Reliability Life Testing And The Prediction Of Service Lives written by Sam C. Saunders and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-26 with Computers categories.

The prerequisite for reading this text is a calculus based course in Probability and Mathematical Statistics, along with the usual curricularmathematical requi- ments for every science major. For graduate students from disciplines other than mathematical sciences much advantage, viz., both insight and mathematical - turity, is gained by having had experience quantifying the assurance for safety of structures, operability of systems or health of persons. It is presumed that each student will have some familiarity with Mathematica or Maple or better yet also have available some survival analysis software such as S Plus or R, to handle the computations with the data sets. This material has been selected under the conviction that the most practical aid any investigator can have is a good theory. The course is intended for p- sons who will, during their professional life, be concerned with the 'theoretical' aspects of applied science. This implies consulting with industrial mathema- cians/statisticians' lead engineers in various fields, physcists, chemists, material scientists and other technical specialists who are collaborating to solve some d- ficult technological/scientific problem. Accordingly, there are sections devoted to the deportment of applied mathematicians during consulting. This corresponds to the 'bedside manner' of physicians and is a important aspect of professionalism.

An Introduction To Copulas

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Author : Roger B. Nelsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-10

An Introduction To Copulas written by Roger B. Nelsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-10 with Mathematics categories.

The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.

The Design And Analysis Of Computer Experiments

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Author : Thomas J. Santner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

The Design And Analysis Of Computer Experiments written by Thomas J. Santner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

In the past 15 to 20 years, the computer has become a popular tool for exploring the relationship between a measured response and factors thought to affect the response. In many cases, scientific theories exist that implicitly relate the response to the factors by means of systems of mathematical equations. There also exist numerical methods for accurately solving such equations and appropriate computer hardware and software to implement these methods. In many engineering applications, for example, the relationship is described by a dynamical system and the numerical method is a finite element code. In such situations, these numerical methods allow one to produce computer code that can generate the response corresponding to any given set of values of the factors. This allows one to conduct an "experiment" (called a "computer experiment") to explore the relationship between the response and the factors using the code. Indeed, in some cases computer experimentation is feasible when a properly designed physical experiment (the gold standard for establishing cause and effect) is impossible. For example, the number of input variables may be too large to consider performing a physical experiment or it may simply be economically prohibitive to run an experiment on the scale required to gather sufficient information to answer a particular research question. This book describes methods for designing and analyzing experiments conducted using computer code in lieu of a physical experiment. It discusses how to select the values of the factors at which to run the code (the design of the computer experiment) in light of the research objectives of the experimenter. It also provides techniques for analyzing the resulting data so as to achieve these research goals.

Statistical Inference For Ergodic Diffusion Processes

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Author : Yury A. Kutoyants
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Statistical Inference For Ergodic Diffusion Processes written by Yury A. Kutoyants and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.