Download or read book Consistency of a Least Squares Orthonormal Series Estimator for a Regression Function written by Michel Delecroix and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthonormal Series Estimators written by Odile Pons and published by World Scientific. This book was released on 2020-01-22 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximation and the estimation of nonparametric functions by projections on an orthonormal basis of functions are useful in data analysis. This book presents series estimators defined by projections on bases of functions, they extend the estimators of densities to mixture models, deconvolution and inverse problems, to semi-parametric and nonparametric models for regressions, hazard functions and diffusions. They are estimated in the Hilbert spaces with respect to the distribution function of the regressors and their optimal rates of convergence are proved. Their mean square errors depend on the size of the basis which is consistently estimated by cross-validation. Wavelets estimators are defined and studied in the same models.The choice of the basis, with suitable parametrizations, and their estimation improve the existing methods and leads to applications to a wide class of models. The rates of convergence of the series estimators are the best among all nonparametric estimators with a great improvement in multidimensional models. Original methods are developed for the estimation in deconvolution and inverse problems. The asymptotic properties of test statistics based on the estimators are also established.
Download or read book Are Regression Series Estimators Efficient in Practice A Computational Comparison Study written by Michel Delecroix and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the practical performances of series-type estimators of a regression function. For different choices of orthonormal bases (Legendre polynomials, trigonometric functions, wavelets) we compare, by simulation arguments, the performances of series-type estimators with the results obtained by two of the most popular nonparametric regression estimation methods: kernel estimation and least-squares cubic splines. It will be shown that orthonormal series estimators are competitive in relation to these former nonparametric procedures. No agreement has emerged on the best method, the results being highly dependent on the nature of the estimated regression function.
Download or read book Applicationes Mathematicae written by and published by . This book was released on 2001 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seemingly Unrelated Regression Equations Models written by Virendera K. Srivastava and published by CRC Press. This book was released on 2020-08-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the scattered literature associated with the seemingly unrelated regression equations (SURE) model used by econometricians and others. It focuses on the theoretical statistical results associated with the SURE model.
Download or read book Nonparametric Regression Analysis of Longitudinal Data written by Hans-Georg Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reviews some of the work that has been done for longitudi nal data in the rapidly expanding field of nonparametric regression. The aim is to give the reader an impression of the basic mathematical tools that have been applied, and also to provide intuition about the methods and applications. Applications to the analysis of longitudinal studies are emphasized to encourage the non-specialist and applied statistician to try these methods out. To facilitate this, FORTRAN programs are provided which carry out some of the procedures described in the text. The emphasis of most research work so far has been on the theoretical aspects of nonparametric regression. It is my hope that these techniques will gain a firm place in the repertoire of applied statisticians who realize the large potential for convincing applications and the need to use these techniques concurrently with parametric regression. This text evolved during a set of lectures given by the author at the Division of Statistics at the University of California, Davis in Fall 1986 and is based on the author's Habilitationsschrift submitted to the University of Marburg in Spring 1985 as well as on published and unpublished work. Completeness is not attempted, neither in the text nor in the references. The following persons have been particularly generous in sharing research or giving advice: Th. Gasser, P. Ihm, Y. P. Mack, V. Mammi tzsch, G . G. Roussas, U. Stadtmuller, W. Stute and R.
Download or read book Journal of Statistical Planning and Inference written by North-Holland Publishing Company and published by . This book was released on 2003 with total page 1304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Consistent Directions of the Least Squares Estimators in Linear Models written by Song-Gui Wang and published by . This book was released on 1982 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The consistent directions of the least squares estimators in a linear model are defined to be the linear combinations of parameter estimates that are asympotically consistent. When the design variable is univariate and the regression function is smooth, consistent directions are characterized in previous papers (Wu, 1980; Wu and Wang, 1982) in terms of the convergence rates of the design sequence to its limit points. Extension of these results to multivariate design variables are considered in the present paper.
Download or read book Modelling and Identification with Rational Orthogonal Basis Functions written by Peter S.C. Heuberger and published by Springer Science & Business Media. This book was released on 2005-06-30 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing. Modelling and Identification with Rational Orthogonal Basis Functions affords a self-contained description of the development of the field over the last 15 years, furnishing researchers and practising engineers working with dynamical systems and stochastic processes with a standard reference work.
Download or read book Introduction to Time Series and Forecasting written by Peter J. Brockwell and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.
Download or read book A Distribution Free Theory of Nonparametric Regression written by László Györfi and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distribution-free properties of the estimates.
Download or read book Properties of Some Preliminary Test Estimators in Regression Using a Quadratic Loss Criterion written by Mary Ellen Bock and published by . This book was released on 1972 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Consistency of Least Squares Estimators in Error Correction Models written by James H. Stock and published by . This book was released on 1984 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterisation of Areal Surface Texture written by Richard Leach and published by Springer Science & Business Media. This book was released on 2013-04-03 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The function of a component part can be profoundly affected by its surface topography. There are many examples in nature of surfaces that have a well-controlled topography to affect their function. Examples include the hydrophobic effect of the lotus leaf, the reduction of fluid drag due to the riblet structure of shark skin, the directional adhesion of the gecko foot and the angular sensitivity of the multi-faceted fly eye. Surface structuring is also being used extensively in modern manufacturing. In this way many properties can be altered, for example optical, tribological, biological and fluidic. Previously, single line (profile) measurements were adequate to control manufacture of surfaces, but as the need to control the functionality of surfaces increases, there is a growing need for three-dimensional (areal) measurement and characterisation techniques. For this reason there has been considerable research, development and standardisation of areal techniques. This book will present the areal framework that is being adopted by the international community. Whereas previous books have concentrated on the measurement aspects, this book concentrates on the characterisation techniques, i.e. how to interpret the measurement data to give the appropriate (functional) information for a given task. The first part of the book presents the characterisation methods and the second part case studies that highlight the use of areal methods in a broad range of subject areas - from automobile manufacture to archaeology. Contents Introduction to Surface Topography The Areal Field Parameters The Areal Feature Parameters Areal Filtering Methods Areal Form Removal Areal Fractal Methods Choosing the Appropriate Parameter Characterisation of Individual Areal Features Multi-Scale Signature of Surface Topography Correlation of Areal Surface Texture Parameters to Solar Cell Efficiency Characterisation of Cylinder Liner Honing Textures for Production Control Characterisation of the Mechanical Bond Strength for Copper on Glass Plating Applications Inspection of Laser Structured Cams and Conrods Road Surfaces
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Intelligent Decision Technologies 2018 written by Ireneusz Czarnowski and published by Springer. This book was released on 2018-05-30 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the proceedings of the KES-IDT-2018 conference, held in Gold Coast, Queensland, Australia, on June 20–22, 2018 The conference provided opportunities to present and discuss the latest research results, promoting knowledge transfer and the generation of new ideas in the field of intelligent decision-making. The range of topics explored is wide, and includes methods for decision-making, decision support, data analysis, modeling and many more in areas such as finance, economics, management, engineering and transportation. The book contains several sections devoted to specific topics, such as: · Decision-Making Theory for Economics · Advances in Knowledge-based Statistical Data Analysis · On Knowledge-Based Digital Ecosystems & Technologies for Smart and Intelligent Decision Support Systems · Soft Computing Models in Industrial and Management Engineering · Computational Media Computing and its Applications · Intelligent Decision-Making Technologies · Digital Architectures and Decision Management
Download or read book Econometrics written by Bruce Hansen and published by Princeton University Press. This book was released on 2022-06-28 with total page 1081 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most authoritative and up-to-date core econometrics textbook available Econometrics is the quantitative language of economic theory, analysis, and empirical work, and it has become a cornerstone of graduate economics programs. Econometrics provides graduate and PhD students with an essential introduction to this foundational subject in economics and serves as an invaluable reference for researchers and practitioners. This comprehensive textbook teaches fundamental concepts, emphasizes modern, real-world applications, and gives students an intuitive understanding of econometrics. Covers the full breadth of econometric theory and methods with mathematical rigor while emphasizing intuitive explanations that are accessible to students of all backgrounds Draws on integrated, research-level datasets, provided on an accompanying website Discusses linear econometrics, time series, panel data, nonparametric methods, nonlinear econometric models, and modern machine learning Features hundreds of exercises that enable students to learn by doing Includes in-depth appendices on matrix algebra and useful inequalities and a wealth of real-world examples Can serve as a core textbook for a first-year PhD course in econometrics and as a follow-up to Bruce E. Hansen’s Probability and Statistics for Economists
