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Best Linear Unbiased And Invariant Estimators For Regression Parameters Based On Ordered Observations
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Book Synopsis Best Linear Unbiased and Invariant Estimators for Regression Parameters Based on Ordered Observations by : Z. Govindarajulu
Download or read book Best Linear Unbiased and Invariant Estimators for Regression Parameters Based on Ordered Observations written by Z. Govindarajulu and published by . This book was released on 1974 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The best linear unbiased estimators of the parameters in the multiple regression model are obtained when the samples are arbitrarily censored. The homogeneity of variance, polynomial regression and simple linear regression become special cases of the above model. The formulas take simpler forms when the underlying distribution is symmetric and the subsamples are of equal size and are symmetrically censored. Best constant-risk estimators of the parameters alpha, beta, and sigma in the simple linear regression model are obtained. These results are applied to symmetric uniform and negative exponential cases. (Author).
Book Synopsis Order Statistics by : Herbert A. David
Download or read book Order Statistics written by Herbert A. David and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones.
Book Synopsis Foundations of Estimation Theory by : L. Kubacek
Download or read book Foundations of Estimation Theory written by L. Kubacek and published by Elsevier. This book was released on 2012-12-02 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapters on linear and quadratic estimations, and normality of observation vectors have been included. Chapter 2 includes selected items of information from algebra, functional analysis and the theory of probability, intended to facilitate the reading of the text proper and to save the reader looking up individual theorems in various textbooks and papers; it is mainly devoted to the reproducing kernel Hilbert spaces, helpful in solving many estimation problems. The text proper of the book begins with Chapter 3. This is divided into two parts: the first deals with sufficient statistics, complete sufficient statistics, minimal sufficient statistics and relations between them; the second contains the mostimportant inequalities of estimation theory for scalar and vector valued parameters and presents properties of the exponential family of distributions.The fourth chapter is an introduction to asymptotic methods of estimation. The method of statistical moments and the maximum-likelihood method are investigated. The sufficient conditions for asymptotical normality of the estimators are given for both methods. The linear and quadratic methods of estimation are dealt with in the fifth chapter. The method of least squares estimation is treated. Five basic regular versions of the regression model and the unified linear model of estimation are described. Unbiased estimators for unit dispersion (factor of the covariance matrix) are given for all mentioned cases. The equivalence of the least-squares method to the method of generalized minimum norm inversion of the design matrix of the regression model is studied in detail. The problem of estimating the covariance components in the mixed model is mentioned as well. Statistical properties of linear and quadratic estimators developed in the fifth chapter in the case of normally distributed errors of measurement are given in Chapter 6. Further, the application of tensor products of Hilbert spaces generated by the covariance matrix of random error vector of observations is demonstrated. Chapter 7 reviews some further important methods of estimation theory. In the first part Wald's method of decision functions is applied to the construction of estimators. The method of contracted estimators and the method of Hoerl and Kennard are presented in the second part. The basic ideas of robustness and Bahadur's approach to estimation theory are presented in the third and fourth parts of this last chapter.
Book Synopsis Applied Statistics by : Rajendra Prasad Gupta
Download or read book Applied Statistics written by Rajendra Prasad Gupta and published by . This book was released on 1975 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :
Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1995 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Book Synopsis Applications of Linear and Nonlinear Models by : Erik W. Grafarend
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.
Book Synopsis Statistics Subject Indexes from Mathematical Reviews by : American Mathematical Society
Download or read book Statistics Subject Indexes from Mathematical Reviews written by American Mathematical Society and published by . This book was released on 1987 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Linear and Nonlinear Models by : Erik Grafarend
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.
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reliability Verification, Testing, and Analysis in Engineering Design by : Gary Wasserman
Download or read book Reliability Verification, Testing, and Analysis in Engineering Design written by Gary Wasserman and published by CRC Press. This book was released on 2002-11-27 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Striking a balance between the use of computer-aided engineering practices and classical life testing, this reference expounds on current theory and methods for designing reliability tests and analyzing resultant data through various examples using Microsoft® Excel, MINITAB, WinSMITH, and ReliaSoft software across multiple industries. The book disc
Book Synopsis Statistical Intervals by : Gerald J. Hahn
Download or read book Statistical Intervals written by Gerald J. Hahn and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed exposition of statistical intervals and emphasizes applications in industry. The discussion differentiates at an elementary level among different kinds of statistical intervals and gives instruction with numerous examples and simple math on how to construct such intervals from sample data. This includes confidence intervals to contain a population percentile, confidence intervals on probability of meeting specified threshold value, and prediction intervals to include observation in a future sample. Also has an appendix containing computer subroutines for nonparametric statistical intervals.
Download or read book Referativnyĭ zhurnal written by and published by . This book was released on 1976 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Response Surfaces, Regression, and Positive Data Analyses by : Rabindra Nath Das
Download or read book Robust Response Surfaces, Regression, and Positive Data Analyses written by Rabindra Nath Das and published by CRC Press. This book was released on 2014-05-21 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although widely used in science and technology for experimental data generating, modeling, and optimization, the response surface methodology (RSM) has many limitations. Showing how robust response surface methodology (RRSM) can overcome these limitations, Robust Response Surfaces, Regression, and Positive Data Analyses presents RRS designs, along with the relevant regression and positive data analysis techniques. It explains how to use RRSM in experimental designs and regression analysis. The book addresses problems of RRS designs, such as rotatability, slope-rotatability, weak rotatability, and optimality. It describes methods for estimating model parameters as well as positive data analysis techniques. The author illustrates the concepts and methods with real examples of lifetime responses, resistivity, replicated measures, and more. The range of topics and applications gives the book broad appeal both to theoreticians and practicing professionals. The book helps quality engineers, scientists in any area, medical practitioners, demographers, economists, and statisticians understand the theory and applications of RRSM. It can also be used in a second course on the design of experiments.
Book Synopsis An Author and Permuted Title Index to Selected Statistical Journals by : Brian L. Joiner
Download or read book An Author and Permuted Title Index to Selected Statistical Journals written by Brian L. Joiner and published by . This book was released on 1970 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 1368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Government Reports Announcements by :
Download or read book Government Reports Announcements written by and published by . This book was released on 1974-11 with total page 966 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Models in Statistics by : Alvin C. Rencher
Download or read book Linear Models in Statistics written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2008-01-07 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
