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Author : K. Mukherjee
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (897 download)
Download or read book Robust Estimation in Nonlinear Regression Via Minimum Distance Method written by K. Mukherjee and published by . This book was released on 1994 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hossein Riazoshams
Publisher : John Wiley & Sons
ISBN 13 : 1118738063
Total Pages : 258 pages
Book Rating : 4.1/5 (187 download)
Download or read book Robust Nonlinear Regression written by Hossein Riazoshams and published by John Wiley & Sons. This book was released on 2018-08-20 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to discuss robust aspects of nonlinear regression—with applications using R software Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression Addresses some commonly mishandled aspects of modeling R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.
Author : Pavel Čížek
Publisher :
ISBN 13 : 9788086288666
Total Pages : 86 pages
Book Rating : 4.2/5 (886 download)
Download or read book Robust Estimation in Nonlinear Regression and Limited Dependent Variable Models written by Pavel Čížek and published by . This book was released on 2001 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Werner Stahel
Publisher : Springer Science & Business Media
ISBN 13 : 1461244447
Total Pages : 384 pages
Book Rating : 4.4/5 (612 download)
Download or read book Directions in Robust Statistics and Diagnostics written by Werner Stahel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications DIRECTIONS IN ROBUST STATISTICS AND DIAGNOSTICS is based on the proceedings of the first four weeks of the six week IMA 1989 summer program "Robustness, Diagnostics, Computing and Graphics in Statistics". An important objective of the organizers was to draw a broad set of statisticians working in robustness or diagnostics into collaboration on the challenging problems in these areas, particularly on the interface between them. We thank the organizers of the robustness and diagnostics program Noel Cressie, Thomas P. Hettmansperger, Peter J. Huber, R. Douglas Martin, and especially Werner Stahel and Sanford Weisberg who edited the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Central themes of all statistics are estimation, prediction, and making decisions under uncertainty. A standard approach to these goals is through parametric mod elling. Parametric models can give a problem sufficient structure to allow standard, well understood paradigms to be applied to make the required inferences. If, how ever, the parametric model is not completely correct, then the standard inferential methods may not give reasonable answers. In the last quarter century, particularly with the advent of readily available computing, more attention has been paid to the problem of inference when the parametric model used is not correctly specified.
Author : William C. Parr
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (227 download)
Download or read book Minimum Distance and Robust Estimation written by William C. Parr and published by . This book was released on 1978 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust and consistent of the location parameter of an asymmetric distribution and general, non-location and scale parameter estimation problems have been vexing problems in the history of robustness studies. The minimum distance (MD) estimation method is shown to provide a heuristically reasonable mode of attack for these problems which also leads to excellent robustness properties. Both asymptotic and Monte Carlo results for the familiar case of estimation of the location parameter of a symmetric distribution support this proposition, showing MD-estimators to be competitive with some of the better estimators thus far proposed. (Author).
Author : Joseph Awange
Publisher : Springer
ISBN 13 : 3319254650
Total Pages : 548 pages
Book Rating : 4.3/5 (192 download)
Download or read book Geospatial Algebraic Computations written by Joseph Awange and published by Springer. This book was released on 2016-01-29 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improved geospatial instrumentation and technology such as in laser scanning has now resulted in millions of data being collected, e.g., point clouds. It is in realization that such huge amount of data requires efficient and robust mathematical solutions that this third edition of the book extends the second edition by introducing three new chapters: Robust parameter estimation, Multiobjective optimization and Symbolic regression. Furthermore, the linear homotopy chapter is expanded to include nonlinear homotopy. These disciplines are discussed first in the theoretical part of the book before illustrating their geospatial applications in the applications chapters where numerous numerical examples are presented. The renewed electronic supplement contains these new theoretical and practical topics, with the corresponding Mathematica statements and functions supporting their computations introduced and applied. This third edition is renamed in light of these technological advancements.
Author : Joseph L. Awange
Publisher : Springer Science & Business Media
ISBN 13 : 3642121241
Total Pages : 380 pages
Book Rating : 4.6/5 (421 download)
Download or read book Algebraic Geodesy and Geoinformatics written by Joseph L. Awange and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: While preparing and teaching ‘Introduction to Geodesy I and II’ to undergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taught required some skills in algebra, and in particular, computer algebra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we have attempted to put together basic concepts of abstract algebra which underpin the techniques for solving algebraic problems. Algebraic computational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds, the concepts and techniques presented herein are nonetheless applicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robotics apply resection and intersection techniques which require algebraic solutions. Solution of nonlinear systems of equations is an indispensable task in almost all geosciences such as geodesy, geoinformatics, geophysics (just to mention but a few) as well as robotics. These equations which require exact solutions underpin the operations of ranging, resection, intersection and other techniques that are normally used. Examples of problems that require exact solutions include; • three-dimensional resection problem for determining positions and orientation of sensors, e. g. , camera, theodolites, robots, scanners etc.
Author :
Publisher :
ISBN 13 :
Total Pages : 554 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Methods of Statistics written by and published by . This book was released on 2003 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Erik W. Grafarend
Publisher : Springer Nature
ISBN 13 : 3030945987
Total Pages : 1127 pages
Book Rating : 4.0/5 (39 download)
Download or read book Applications of Linear and Nonlinear Models written by Erik W. Grafarend and published by Springer Nature. This book was released on 2022-10-01 with total page 1127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss–Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann–Plucker coordinates, criterion matrices of type Taylor–Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models. The chapter on algebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.
Author : Jana Jurecková
Publisher : John Wiley & Sons
ISBN 13 : 9780471822219
Total Pages : 496 pages
Book Rating : 4.8/5 (222 download)
Download or read book Robust Statistical Procedures written by Jana Jurecková and published by John Wiley & Sons. This book was released on 1996-04-19 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad and unified methodology for robust statistics—with exciting new applications Robust statistics is one of the fastest growing fields in contemporary statistics. It is also one of the more diverse and sometimes confounding areas, given the many different assessments and interpretations of robustness by theoretical and applied statisticians. This innovative book unifies the many varied, yet related, concepts of robust statistics under a sound theoretical modulation. It seamlessly integrates asymptotics and interrelations, and provides statisticians with an effective system for dealing with the interrelations between the various classes of procedures. Drawing on the expertise of researchers from around the world, and covering over a decade's worth of developments in the field, Robust Statistical Procedures: Asymptotics and Interrelations: Discusses both theory and applications in its two parts, from the fundamentals to robust statistical inference Thoroughly explores the interrelations between diverse classes of procedures, unlike any other book Compares nonparametric procedures with robust statistics, explaining in detail asymptotic representations for various estimators Provides a timesaving list of mathematical tools for the problems under discussion Keeps mathematical abstractions to a minimum, in spite of its largely theoretical content Includes useful problems and exercises at the end of each chapter Offers strategies for more complex models when using robust statistical procedures Self-contained and rounded in approach, this book is invaluable for both applied statisticians and theoretical researchers; for graduate students in mathematical statistics; and for anyone interested in the influence of this methodology.
Author : Pavel Čížek
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (762 download)
Download or read book Robust Estimation in Nonlinear Regression Models written by Pavel Čížek and published by . This book was released on 2001 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Erik Grafarend
Publisher : Springer Science & Business Media
ISBN 13 : 3642222412
Total Pages : 1026 pages
Book Rating : 4.6/5 (422 download)
Download or read book Applications of Linear and Nonlinear Models written by Erik Grafarend and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.
Author : Helga Bunke
Publisher :
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.:/5 (321 download)
Download or read book Nonlinear Regression, Functional Relations and Robust Methods written by Helga Bunke and published by . This book was released on 1989 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the second volume in a three part work, provides a comprehensive and unified account of nonlinear regression analysis, functional and structural relations, and of nonparametric and robust estimators. Research in these areas has been stimulated by the increase in computational capabilities and this volume will therefore be of great interest to researchers in statistics as well as applied statisticians working in industry. The material provided includes recent work from German and Russian sources, as well as from English-speaking sources, and the treatment throughout is mathematically rigorous but accessible. The text will benefit rsearchers in statistics and applied statisticians working in industry.
Author : Joseph L. Awange
Publisher : Springer Science & Business Media
ISBN 13 : 9783540234258
Total Pages : 352 pages
Book Rating : 4.2/5 (342 download)
Download or read book Solving Algebraic Computational Problems in Geodesy and Geoinformatics written by Joseph L. Awange and published by Springer Science & Business Media. This book was released on 2005 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charity Mupanga, the resilient and maternal proprietor of Harrods International Bar (and Nightspot) faces her toughest challenge in Dizzy Worms, the final novel in Michael Holman's acclaimed trilogy set in the African slum of Kireba. Faced with a Health and Safety closure, Charity has a week to appeal and the chances of success seem negligible: elections are imminent, and Kireba is due to become a showcase of President Josiah Nduka's 'slum rehabilitation program', backed by gullible foreign donors. But before taking on Nduka and the council, she has a promise to keep – to provide a supply of her famous sweet doughballs to a small army of street children, as voracious as they are malodorous . . . Michael Holman uses his witty satirical pen to brilliant effect in this affectionate portrait of a troubled region, targeting local politicians, western diplomats, foreign donors and journalists, puncturing pretensions and questioning the philosophy of aid.
Author : Aysegul Dastan
Publisher : Stanford University
ISBN 13 :
Total Pages : 265 pages
Book Rating : 4.F/5 ( download)
Download or read book A New Look at Nonlinear Regression in Well Testing written by Aysegul Dastan and published by Stanford University. This book was released on 2010 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we made significant improvements to nonlinear regression used in well test interpretation. Nonlinear regression was introduced to well testing more than three decades ago and quickly became a standard practice in the industry. However, limited improvement has been achieved for some time. This widely-used technique is vulnerable to issues commonly observed in real data sets, namely sensitivity to noise, parameter uncertainty (ambiguity), and dependence on starting guess. We developed several different methods that improved nonlinear regression significantly. We investigated the performance of these methods on a variety of field data to determine which method (or combination of methods) works best in particular well test situations. The techniques we developed can be considered in three groups: In the first group we considered parameter transformations. We developed techniques to find robust Cartesian transform pairs that worked very well with a variety of reservoir models. The Cartesian parameter transformations we proposed provided faster convergence, doubled the probability of convergence for a random starting guess, and revealed the ambiguities inherent in the data. In the second group, data space transformations, we analyzed the wavelet transform and the pressure derivative. We developed four different strategies to form a reduced wavelet basis and conducted nonlinear regression in the reduced basis rather than the original pressure data points. Using these strategies we achieved improved performance in terms of likelihood of convergence and narrower confidence intervals (reduced uncertainty). We also developed a novel interpretation technique for cyclic data analysis. The technique is based on the two-dimensional wavelet transform and takes into account the correlation between subsequent cycles for error correction. We also considered derivative curve analysis as another form of data space transformation. Derivative fitting was found to improve confidence intervals significantly and provide faster convergence for dual-porosity reservoirs. We also showed the necessity of using the Monte Carlo simulation technique for accurate computation of confidence intervals for dual-porosity reservoirs. In the third group of nonlinear regression techniques we considered alternative objective functions to regular least squares. We developed a robust total least squares (TLS) algorithm that considers and minimizes deviations in both time and pressure simultaneously, hence making interpretation results more accurate and more stable. When there are deviations in the time data TLS performs substantially better than least squares, giving much narrower confidence intervals. In addition, the total least squares approach was found to be less prone to time-shift errors and errors in the early time data. We also considered the least absolute value (LAV) technique as an alternative to the least squares objective function. Using orthogonal distance regression together with the least absolute value criterion, we achieved a robust estimator for data with time deviations and outliers. We developed an analysis technique based on the sum of square roots. The least square root technique was found to be robust against nonideality in data. We tested the techniques rigorously by using a large matrix of test cases made up of real and generated well test data sets. In the test matrix all possible combinations of different methods were applied to 20 real well test data sets from a selection of reservoir models and test scenarios, including dual-porosity and fractured reservoirs, reservoirs with rectangular boundaries, cyclic buildup-drawdown tests, and general multirate data. We determined the methods or combinations of methods that work best with a particular reservoir model. We expect that our techniques will provide more accurate estimation of reservoir parameters, allowing for better forecasting of reservoir performance.
Author : Peter .J. Bickel
Publisher : CRC Press
ISBN 13 : 9780534980443
Total Pages : 478 pages
Book Rating : 4.9/5 (84 download)
Download or read book A Festschrift For Erich L. Lehmann written by Peter .J. Bickel and published by CRC Press. This book was released on 1982-02-01 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of essays and articles In honour of Erich. L. Lehmann's sixty-fifth birthday. Including works on Vector Autoregressive models, Bootstrapping Regression Models, Bootstrapping Regression Models and Estimation of the Mean or Total when Measurement Protocols.
Author : Helga Bunke
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.3/5 (91 download)
Download or read book Statistical Methods of Model Building: Nonlinear regression, functional relations, and robust methods written by Helga Bunke and published by . This book was released on 1986 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
