The Population-sample Decomposition Approach to Multivariate Estimation Methods PDF Download
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Author: Bernard M. S. van Praag
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
Author: Bernard M. S. van Praag
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
Author: A.M. Wesselman
Publisher: Springer Science & Business Media
ISBN: 9400936796
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Author: Albertus Martinus Wesselman
Publisher:
ISBN: 9789024727308
Category : Estimation theory
Languages : en
Pages : 0
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Book Description
Author: A. M. Wesselman
Publisher:
ISBN: 9789024727308
Category : Multivariate analysis
Languages : en
Pages : 0
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Book Description
Author: Albertus M. Wesselman
Publisher:
ISBN:
Category :
Languages : nl
Pages :
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 129
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Book Description
Estimation of population covariance matrices from samples of multivariate data is of great importance. When the dimension of a covariance matrix is large but the sample size is limited, it is well known that the sample covariance matrix is dissatisfactory. However, the improvement of covariance matrix estimation is not straightforward, mainly because of the constraint of positive definiteness. This thesis work considers decomposition-based methods to circumvent this primary difficulty. Two ways of covariance matrix estimation with regularization on factor matrices from decompositions are included. One approach replies on the modified Cholesky decomposition from Pourahmadi, and the other technique, matrix exponential or matrix logarithm, is closely related to the spectral decomposition. We explore the usage of covariance matrix estimation by imposing L1 regularization on the entries of Cholesky factor matrices, and find the estimates from this approach are not sensitive to the orders of variables. A given order of variables is the prerequisite in the application of the modified Cholesky decomposition, while in practice, information on the order of variables is often unknown. We take advantage of this property to remove the requirement of order information, and propose an order-invariant covariance matrix estimate by refining estimates corresponding to different orders of variables. The refinement not only guarantees the positive definiteness of the estimated covariance matrix, but also is applicable in general situations without the order of variables being pre-specified. The refined estimate can be approximated by only combining a moderate number of representative estimates. Numerical simulations are conducted to evaluate the performance of the proposed method in comparison with several other estimates. By applying the matrix exponential technique, the problem of estimating positive definite covariance matrices is transformed into a problem of estimating symmetric matrices. There are close connections between covariance matrices and their logarithm matrices, and thus, pursing a matrix logarithm with certain properties helps restoring the original covariance matrix. The covariance matrix estimate from applying L1 regularization to the entries of the matrix logarithm is compared to some other estimates in simulation studies and real data analysis.
Author: Hulya Cingi
Publisher: Bentham Science Publishers
ISBN: 1608050122
Category : Mathematics
Languages : en
Pages : 129
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Book Description
"Ratio Method of Estimation - This is an ideal textbook for researchers interested in sampling methods, survey methodologists in government organizations, academicians, and graduate students in statistics, mathematics and biostatistics. This textbook makes"
Author: Paul S. Levy
Publisher: John Wiley & Sons
ISBN: 047040101X
Category : Medical
Languages : en
Pages : 213
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Book Description
A trusted classic on the key methods in population sampling—now in a modernized and expanded new edition Sampling of Populations, Fourth Edition continues to serve as an all-inclusive resource on the basic and most current practices in population sampling. Maintaining the clear and accessible style of the previous edition, this book outlines the essential statistical methodsfor survey design and analysis, while also exploring techniques that have developed over the past decade. The Fourth Edition successfully guides the reader through the basic concepts and procedures that accompany real-world sample surveys, such as sampling designs, problems of missing data, statistical analysis of multistage sampling data, and nonresponse and poststratification adjustment procedures. Rather than employ a heavily mathematical approach, the authors present illustrative examples that demonstrate the rationale behind common steps in the sampling process, from creating effective surveys to analyzing collected data. Along with established methods, modern topics are treated through the book's new features, which include: A new chapter on telephone sampling, with coverage of declining response rates, the creation of "do not call" lists, and the growing use of cellular phones A new chapter on sample weighting that focuses on adjustments to weight for nonresponse, frame deficiencies, and the effects of estimator instability An updated discussion of sample survey data analysis that includes analytic procedures for estimation and hypothesis testing A new section on Chromy's widely used method of taking probability proportional to size samples with minimum replacement of primary sampling units An expanded index with references on the latest research in the field All of the book's examples and exercises can be easily worked out using various software packages including SAS, STATA, and SUDAAN, and an extensive FTP site contains additional data sets. With its comprehensive presentation and wealth of relevant examples, Sampling of Populations, Fourth Edition is an ideal book for courses on survey sampling at the upper-undergraduate and graduate levels. It is also a valuable reference for practicing statisticians who would like to refresh their knowledge of sampling techniques.
Author: Alvin C. Rencher
Publisher: John Wiley & Sons
ISBN: 0471461725
Category : Mathematics
Languages : en
Pages : 739
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Book Description
Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Methods of Multivariate Analysis was among those chosen. When measuring several variables on a complex experimental unit, it is often necessary to analyze the variables simultaneously, rather than isolate them and consider them individually. Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. The Second Edition of Alvin Rencher's Methods of Multivariate Analysis provides students of all statistical backgrounds with both the fundamental and more sophisticated skills necessary to master the discipline. To illustrate multivariate applications, the author provides examples and exercises based on fifty-nine real data sets from a wide variety of scientific fields. Rencher takes a "methods" approach to his subject, with an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. The Second Edition contains revised and updated chapters from the critically acclaimed First Edition as well as brand-new chapters on: Cluster analysis Multidimensional scaling Correspondence analysis Biplots Each chapter contains exercises, with corresponding answers and hints in the appendix, providing students the opportunity to test and extend their understanding of the subject. Methods of Multivariate Analysis provides an authoritative reference for statistics students as well as for practicing scientists and clinicians.
Author: Wojtek Krzanowski
Publisher: OUP Oxford
ISBN: 9780198507086
Category : Mathematics
Languages : en
Pages : 608
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Book Description
Multivariate analysis is necessary whenever more than one characteristic is observed on each individual under study. Applications arise in very many areas of study. This book provides a comprehensive introduction to available techniques for analysing date of this form, written in a style that should appeal to non-specialists as well as to statisticians. In particular, geometric intuition is emphasized in preference to algebraic manipulation wherever possible. The new edition includes a survey of the most recent developments in the subject.
