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Bias Reduction in Functional Estimation by Lei Sun Pdf
New kernel distribution function and kernel density function estimators based on a nonparametric transformation of the data for the purpose of bias reduction are proposed. Asymptotic bias expansions for the new estimators are presented and analyzed. Statistical properties in terms of bias, variance, and mean squared error of the new estimators are investigated with computer simulations.
An Introduction to Bartlett Correction and Bias Reduction by Gauss M. Cordeiro,Francisco Cribari-Neto Pdf
This book presents a concise introduction to Bartlett and Bartlett-type corrections of statistical tests and bias correction of point estimators. The underlying idea behind both groups of corrections is to obtain higher accuracy in small samples. While the main focus is on corrections that can be analytically derived, the authors also present alternative strategies for improving estimators and tests based on bootstrap, a data resampling technique and discuss concrete applications to several important statistical models.
Nonparametric Functional Estimation and Related Topics by George Roussas Pdf
About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.
Functional Estimation for Density, Regression Models and Processes by Odile Pons Pdf
This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators. It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators. Contents:IntroductionKernel Estimator of a DensityKernel Estimator of a Regression FunctionLimits for the Varying Bandwidths EstimatorsNonparametric Estimation of QuantilesNonparametric Estimation of Intensities for Stochastic ProcessesEstimation in Semi-Parametric Regression ModelsDiffusion ProcessesApplications to Time Series Readership: Advanced undergraduate and graduate students in mathematical statistics and computational statistics; researchers in mathematical or applied statistics; statisticians. Keywords:Kernel Estimation;Density;Regression;Intensity;Diffusion;Nonparametric;Weak Convergence;Ergodic Process;Intensity of Point Process;Kernel Estimation;Single-Index Models;Functional Time Series;Variable BandwidthKey Features:Covers a wide range of nonparametric models and presents new functional estimatorsContains a detailed presentation of the mathematical techniques for functional estimation with recent advances in their optimizationA valuable resource for scientific researchers who model observation dataReviews: “This book is useful for researchers interested in the study of asymptotic properties of different types of optimum estimators obtained through the method of kernels.” Mathematical Reviews
Analysis of Variance for Functional Data by Jin-Ting Zhang Pdf
Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data. Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests. Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.
Distance Sampling: Methods and Applications by S. T. Buckland,E.A. Rexstad,T.A. Marques,C.S. Oedekoven Pdf
In this book, the authors cover the basic methods and advances within distance sampling that are most valuable to practitioners and in ecology more broadly. This is the fourth book dedicated to distance sampling. In the decade since the last book published, there have been a number of new developments. The intervening years have also shown which advances are of most use. This self-contained book covers topics from the previous publications, while also including recent developments in method, software and application. Distance sampling refers to a suite of methods, including line and point transect sampling, in which animal density or abundance is estimated from a sample of distances to detected individuals. The book illustrates these methods through case studies; data sets and computer code are supplied to readers through the book’s accompanying website. Some of the case studies use the software Distance, while others use R code. The book is in three parts. The first part addresses basic methods, the design of surveys, distance sampling experiments, field methods and data issues. The second part develops a range of modelling approaches for distance sampling data. The third part describes variations in the basic method; discusses special issues that arise when sampling different taxa (songbirds, seabirds, cetaceans, primates, ungulates, butterflies, and plants); considers advances to deal with failures of the key assumptions; and provides a check-list for those conducting surveys.
Applied Nonparametric Statistics in Reliability by M. Luz Gámiz,K. B. Kulasekera,Nikolaos Limnios,Bo Henry Lindqvist Pdf
Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. It is nevertheless true that, whereas these methods have already proved highly effective in other applied areas of knowledge such as biostatistics or social sciences, nonparametric analyses in reliability currently form an interesting area of study that has not yet been fully explored. Applied Nonparametric Statistics in Reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. The scope of the book includes: smooth estimation of the reliability function and hazard rate of non-repairable systems; study of stochastic processes for modelling the time evolution of systems when imperfect repairs are performed; nonparametric analysis of discrete and continuous time semi-Markov processes; isotonic regression analysis of the structure function of a reliability system, and lifetime regression analysis. Besides the explanation of the mathematical background, several numerical computations or simulations are presented as illustrative examples. The corresponding computer-based methods have been implemented using R and MATLAB®. A concrete modelling scheme is chosen for each practical situation and, in consequence, a nonparametric inference procedure is conducted. Applied Nonparametric Statistics in Reliability will serve the practical needs of scientists (statisticians and engineers) working on applied reliability subjects.
Fundamentals of Signal Processing for Sound and Vibration Engineers by Kihong Shin,Joseph Hammond Pdf
Fundamentals of Signal Processing for Sound and Vibration Engineers is based on Joe Hammond’s many years of teaching experience at the Institute of Sound and Vibration Research, University of Southampton. Whilst the applications presented emphasise sound and vibration, the book focusses on the basic essentials of signal processing that ensures its appeal as a reference text to students and practitioners in all areas of mechanical, automotive, aerospace and civil engineering. Offers an excellent introduction to signal processing for students and professionals in the sound and vibration engineering field. Split into two parts, covering deterministic signals then random signals, and offering a clear explanation of their theory and application together with appropriate MATLAB examples. Provides an excellent study tool for those new to the field of signal processing. Integrates topics within continuous, discrete, deterministic and random signals to facilitate better understanding of the topic as a whole. Illustrated with MATLAB examples, some using ‘real’ measured data, as well as fifty MATLAB codes on an accompanying website.
Features papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. This work focuses on various types of spline estimations and convolution problems.
Rationality, Bounded Rationality and Microfoundations by R. Salehnejad Pdf
This book challenges the generally accepted theories of classical economics, explaining why the expected utility theory, even if it were true, fails to be of much help in solving economic controversies.
Nonparametric Function Estimation, Modeling, and Simulation by James R. Thompson,Richard A. Tapia Pdf
Topics emphasized in this book include nonparametric density estimation, multi-dimensional data analysis, cancer progression, chaos theory, and parallel based algorithms.
Advanced Modelling in Mathematical Finance by Jan Kallsen,Antonis Papapantoleon Pdf
This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.
The Bootstrap and Edgeworth Expansion by Peter Hall Pdf
This monograph addresses two quite different topics, each being able to shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap. The book is aimed at graduate level for those with some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter such that mathematically able readers without knowledge of the rigorous theory of probability will have no trouble understanding most of the book.
Applied Categorical and Count Data Analysis by Wan Tang,Hua He,Xin M. Tu Pdf
Developed from the authors’ graduate-level biostatistics course, Applied Categorical and Count Data Analysis, Second Edition explains how to perform the statistical analysis of discrete data, including categorical and count outcomes. The authors have been teaching categorical data analysis courses at the University of Rochester and Tulane University for more than a decade. This book embodies their decade-long experience and insight in teaching and applying statistical models for categorical and count data. The authors describe the basic ideas underlying each concept, model, and approach to give readers a good grasp of the fundamentals of the methodology without relying on rigorous mathematical arguments. The second edition covers classic concepts and popular topics, such as contingency tables, logistic regression models, and Poisson regression models, along with modern areas that include models for zero-modified count outcomes, parametric and semiparametric longitudinal data analysis, reliability analysis, and methods for dealing with missing values. As in the first edition, R, SAS, SPSS, and Stata programming codes are provided for all the examples, enabling readers to immediately experiment with the data in the examples and even adapt or extend the codes to fit data from their own studies. Designed for a one-semester course for graduate and senior undergraduate students in biostatistics, this self-contained text is also suitable as a self-learning guide for biomedical and psychosocial researchers. It will help readers analyze data with discrete variables in a wide range of biomedical and psychosocial research fields. Features: Describes the basic ideas underlying each concept and model Includes R, SAS, SPSS and Stata programming codes for all the examples Features significantly expanded Chapters 4, 5, and 8 (Chapters 4-6, and 9 in the second edition Expands discussion for subtle issues in longitudinal and clustered data analysis such as time varying covariates and comparison of generalized linear mixed-effect models with GEE
