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Asymptotic Theory For Canonical Correlation Analysis
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Book Synopsis Asymptotic Theory for Canonical Correlation Analysis by : Theodore Wilbur Anderson
Download or read book Asymptotic Theory for Canonical Correlation Analysis written by Theodore Wilbur Anderson and published by . This book was released on 1997 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Distributions of Latent Roots in Canonical Correlation Analysis and in Discriminan Analysis with Applications to Testing and Estimation by : William James Glynn
Download or read book Asymptotic Distributions of Latent Roots in Canonical Correlation Analysis and in Discriminan Analysis with Applications to Testing and Estimation written by William James Glynn and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic distribution of latent roots in canonical correlation analysis by : William J. Glynn
Download or read book Asymptotic distribution of latent roots in canonical correlation analysis written by William J. Glynn and published by . This book was released on 1977 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Higher Order Asymptotic Theory for Time Series Analysis by : Masanobu Taniguchi
Download or read book Higher Order Asymptotic Theory for Time Series Analysis written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Book Synopsis Asymptotic Distributions of Latent Roots in Canonical Correlation Analysis and in Discriminant Analysis with Applications to Testing and Estimation by : William James Glynn
Download or read book Asymptotic Distributions of Latent Roots in Canonical Correlation Analysis and in Discriminant Analysis with Applications to Testing and Estimation written by William James Glynn and published by . This book was released on 1979 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Canonical Correlation Analysis in Speech Enhancement by : Jacob Benesty
Download or read book Canonical Correlation Analysis in Speech Enhancement written by Jacob Benesty and published by Springer. This book was released on 2017-08-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the application of canonical correlation analysis (CCA) to speech enhancement using the filtering approach. The authors explain how to derive different classes of time-domain and time-frequency-domain noise reduction filters, which are optimal from the CCA perspective for both single-channel and multichannel speech enhancement. Enhancement of noisy speech has been a challenging problem for many researchers over the past few decades and remains an active research area. Typically, speech enhancement algorithms operate in the short-time Fourier transform (STFT) domain, where the clean speech spectral coefficients are estimated using a multiplicative gain function. A filtering approach, which can be performed in the time domain or in the subband domain, obtains an estimate of the clean speech sample at every time instant or time-frequency bin by applying a filtering vector to the noisy speech vector. Compared to the multiplicative gain approach, the filtering approach more naturally takes into account the correlation of the speech signal in adjacent time frames. In this study, the authors pursue the filtering approach and show how to apply CCA to the speech enhancement problem. They also address the problem of adaptive beamforming from the CCA perspective, and show that the well-known Wiener and minimum variance distortionless response (MVDR) beamformers are particular cases of a general class of CCA-based adaptive beamformers.
Book Synopsis Asymptotics in Statistics and Probability by : Madan L. Puri
Download or read book Asymptotics in Statistics and Probability written by Madan L. Puri and published by VSP. This book was released on 2000-01-01 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Theory Of Quantum Statistical Inference: Selected Papers by : Masahito Hayashi
Download or read book Asymptotic Theory Of Quantum Statistical Inference: Selected Papers written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Book Synopsis Analysis of Multivariate and High-Dimensional Data by : Inge Koch
Download or read book Analysis of Multivariate and High-Dimensional Data written by Inge Koch and published by Cambridge University Press. This book was released on 2014 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.
Book Synopsis Nonlinear Canonical Correlation and Some Related Techniques by : Eeke van der Burg
Download or read book Nonlinear Canonical Correlation and Some Related Techniques written by Eeke van der Burg and published by . This book was released on 1988 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Canonical Correlation Analysis and Network Data Modeling by : Zhuang Ma
Download or read book Canonical Correlation Analysis and Network Data Modeling written by Zhuang Ma and published by . This book was released on 2017 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical decision theory evaluates an estimator mostly by its statistical properties, either the closeness to the underlying truth or the predictive ability for new observations. The goal is to find estimators to achieve statistical optimality. Modern "Big Data" applications, however, necessitate efficient processing of large-scale ("big-n-big-p") datasets, which poses great challenge to classical decision-theoretic framework which seldom takes into account the scalability of estimation procedures. On the one hand, statistically optimal estimators could be computationally intensive and on the other hand, fast estimation procedures might suffer from a loss of statistical efficiency. So the challenge is to kill two birds with one stone. This thesis brings together statistical and computational perspectives to study canonical correlation analysis (CCA) and network data modeling, where we investigate both the optimality and the scalability of the estimators. Interestingly, in both cases, we find iterative estimation procedures based on non-convex optimization can significantly reduce the computational cost and meanwhile achieve desirable statistical properties.In the first part of the thesis, motivated by the recent success of using CCA to learn low-dimensional feature representations of high-dimensional objects, we propose novel metrics which quantify the estimation loss of CCA by the excess prediction loss defined through a prediction-after-dimension-reduction framework. These new metrics have rich statistical and geometric interpretations, which suggest viewing CCA estimation as estimating the subspaces spanned by the canonical variates. We characterize, with minimal assumptions, the non-asymptotic minimax rates under the proposed error metrics, especially how the minimax rates depend on the key quantities including the dimensions, the condition number of the covariance matrices and the canonical correlations. Finally, by formulating sample CCA as a non-convex optimization problem, we propose an efficient (stochastic) first order algorithm which scales to large datasets.In the second part of the thesis, we propose two universal fitting algorithms for networks (possibly with edge covariates) under latent space models: one based on finding the exact maximizer of a convex surrogate of the non-convex likelihood function and the other based on finding an approximate optimizer of the original non-convex objective. Both algorithms are motivated by a special class of inner-product models but are shown to work for a much wider range of latent space models which allow the latent vectors to determine the connection probability of the edges in flexible ways. We derive the statistical rates of convergence of both algorithms and characterize the basin-of-attraction of the non-convex approach. The effectiveness and efficiency of the non-convex procedure is demonstrated by extensive simulations and real-data experiments.
Book Synopsis Robust Correlation by : Georgy L. Shevlyakov
Download or read book Robust Correlation written by Georgy L. Shevlyakov and published by John Wiley & Sons. This book was released on 2016-09-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields. Focuses on implementation of methodology and application of robust correlation with R. Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions. Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates. Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data. Includes an accompanying website featuring computer code and datasets Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.
Book Synopsis Analysis of Multiple Dependent Variables by : Patrick Dattalo
Download or read book Analysis of Multiple Dependent Variables written by Patrick Dattalo and published by Oxford University Press. This book was released on 2013-03-14 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate procedures allow social workers and other human services researchers to analyze complex, multidimensional social problems and interventions in ways that minimize oversimplification. This pocket guide provides a concise, practical, and economical introduction to four procedures for the analysis of multiple dependent variables: multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA), multivariate multiple regression (MMR), and structural equation modeling (SEM). Each procedure will be presented in a way that allows readers to compare and contrast them in terms of (1) appropriate research context; (2) required statistical assumptions, including levels of measurement of variables to be modeled; (3) analytical steps; (4) sample size; and (5) strengths and weaknesses. This invaluable guide facilitates course extensibility in scope and depth by allowing instructors to supplement course content with rigorous statistical procedures. Detailed annotated examples using Stata, SPSS (PASW), SAS, and Amos, together with additional resources, discussion of key terms, and a companion website, make this an unintimidating guide for producers and consumers of social work research knowledge.
Book Synopsis Measurement and Multivariate Analysis by : Shizuhiko Nishisato
Download or read book Measurement and Multivariate Analysis written by Shizuhiko Nishisato and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diversity is characteristic of the information age and also of statistics. To date, the social sciences have contributed greatly to the development of handling data under the rubric of measurement, while the statistical sciences have made phenomenal advances in theory and algorithms. Measurement and Multivariate Analysis promotes an effective interplay between those two realms of research-diversity with unity. The union and the intersection of those two areas of interest are reflected in the papers in this book, drawn from an international conference in Banff, Canada, with participants from 15 countries. In five major categories - scaling, structural analysis, statistical inference, algorithms, and data analysis - readers will find a rich variety of topics of current interest in the extended statistical community.
Book Synopsis Canonical Analysis: Some Relations Between Canonical Correlation, Factor Analysis, Discriminant Function Analysis, and Scaling Theory by : James John McKeon
Download or read book Canonical Analysis: Some Relations Between Canonical Correlation, Factor Analysis, Discriminant Function Analysis, and Scaling Theory written by James John McKeon and published by . This book was released on 1967 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Population-Sample Decomposition Method by : A.M. Wesselman
Download or read book The Population-Sample Decomposition Method written by A.M. Wesselman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Canonical Correlation Analysis by : Bruce Thompson
Download or read book Canonical Correlation Analysis written by Bruce Thompson and published by SAGE. This book was released on 1984-11 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances both in statistical methodology and in computer automation are making canonical correlation analysis available to more and more researchers. In an essentially nonmathematical presentation that provides numerous examples, this volume explains the basic features of this sophisticated technique. Learn more about "The Little Green Book" - QASS Series! Click Here