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Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference Author Michael R. Kosorok
ISBN-10 0387749780
Release 2007-12-29
Pages 483
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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Weak Convergence and Empirical Processes

Weak Convergence and Empirical Processes Author A.W. van der vaart
ISBN-10 9781475725452
Release 2013-03-09
Pages 510
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This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

Lectures on Empirical Processes

Lectures on Empirical Processes Author Eustasio Del Barrio
ISBN-10 9783037190272
Release 2007-01-01
Pages 254
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Lectures on Empirical Processes has been writing in one form or another for most of life. You can find so many inspiration from Lectures on Empirical Processes also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Lectures on Empirical Processes book for free.

Efficient and Adaptive Estimation for Semiparametric Models

Efficient and Adaptive Estimation for Semiparametric Models Author Peter J. Bickel
ISBN-10 9780387984735
Release 1998-06-01
Pages 588
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This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.

Empirical Process Techniques for Dependent Data

Empirical Process Techniques for Dependent Data Author Herold Dehling
ISBN-10 9781461200994
Release 2012-12-06
Pages 383
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Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,

Asymptotic Methods in Statistical Decision Theory

Asymptotic Methods in Statistical Decision Theory Author Lucien Le Cam
ISBN-10 9781461249467
Release 2012-12-06
Pages 742
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This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.

Information and Complexity in Statistical Modeling

Information and Complexity in Statistical Modeling Author Jorma Rissanen
ISBN-10 9780387688121
Release 2007-12-15
Pages 142
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No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.

Asymptotic Statistics

Asymptotic Statistics Author A. W. van der Vaart
ISBN-10 0521784506
Release 2000-06-19
Pages 443
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A mathematically rigorous, practical introduction presenting standard topics plus research.

Adaptive Treatment Strategies in Practice Planning Trials and Analyzing Data for Personalized Medicine

Adaptive Treatment Strategies in Practice  Planning Trials and Analyzing Data for Personalized Medicine Author Michael R. Kosorok
ISBN-10 9781611974188
Release 2015-12-08
Pages 348
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Personalized medicine is a medical paradigm that emphasizes systematic use of individual patient information to optimize that patient's health care, particularly in managing chronic conditions and treating cancer. In the statistical literature, sequential decision making is known as an adaptive treatment strategy (ATS) or a dynamic treatment regime (DTR). The field of DTRs emerges at the interface of statistics, machine learning, and biomedical science to provide a data-driven framework for precision medicine. The authors provide a learning-by-seeing approach to the development of ATSs, aimed at a broad audience of health researchers. All estimation procedures used are described in sufficient heuristic and technical detail so that less quantitative readers can understand the broad principles underlying the approaches. At the same time, more quantitative readers can implement these practices. This book provides the most up-to-date summary of the current state of the statistical research in personalized medicine; contains chapters by leaders in the area from both the statistics and computer sciences fields; and also contains a range of practical advice, introductory and expository materials, and case studies.

Introduction to Stochastic Processes

Introduction to Stochastic Processes Author Erhan Cinlar
ISBN-10 9780486276328
Release 2013-02-20
Pages 416
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Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.

Empirical Processes in M Estimation

Empirical Processes in M Estimation Author Sara A. Geer
ISBN-10 052165002X
Release 2000-01-28
Pages 286
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Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.

Nonparametric and Semiparametric Models

Nonparametric and Semiparametric Models Author Wolfgang Härdle
ISBN-10 9783642171468
Release 2012-08-27
Pages 300
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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.

Functional and Shape Data Analysis

Functional and Shape Data Analysis Author Anuj Srivastava
ISBN-10 9781493940202
Release 2016-10-03
Pages 447
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This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Targeted Learning

Targeted Learning Author Mark J. van der Laan
ISBN-10 1441997822
Release 2011-06-17
Pages 628
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The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest. This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.

A Practical Guide to Splines

A Practical Guide to Splines Author Carl de Boor
ISBN-10 9780387953663
Release 2001-12-01
Pages 348
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This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs.

Biased Sampling Over identified Parameter Problems and Beyond

Biased Sampling  Over identified Parameter Problems and Beyond Author Jing Qin
ISBN-10 9789811048562
Release 2017-06-19
Pages 624
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This book is devoted to biased sampling problems (also called choice-based sampling in Econometrics parlance) and over-identified parameter estimation problems. Biased sampling problems appear in many areas of research, including Medicine, Epidemiology and Public Health, the Social Sciences and Economics. The book addresses a range of important topics, including case and control studies, causal inference, missing data problems, meta-analysis, renewal process and length biased sampling problems, capture and recapture problems, case cohort studies, exponential tilting genetic mixture models etc. The goal of this book is to make it easier for Ph. D students and new researchers to get started in this research area. It will be of interest to all those who work in the health, biological, social and physical sciences, as well as those who are interested in survey methodology and other areas of statistical science, among others.

Statistical Inference for Financial Engineering

Statistical Inference for Financial Engineering Author Masanobu Taniguchi
ISBN-10 9783319034973
Release 2014-03-26
Pages 118
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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.