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New Developments In Multiple Testing And Multivariate Testing For High Dimensional Data
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Book Synopsis New Developments in Multiple Testing and Multivariate Testing for High-dimensional Data by : Zongliang Hu
Download or read book New Developments in Multiple Testing and Multivariate Testing for High-dimensional Data written by Zongliang Hu and published by . This book was released on 2018 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis aims to develop some new and novel methods in advancing multivariate testing and multiple testing for high-dimensional small sample size data. In Chapter 2, we propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Monte Carlo simulations and a real data analysis are also carried out to demonstrate the advantages of the proposed methods. In Chapter 3, we propose a pairwise Hotelling's method for testing high-dimensional mean vectors. The new test statistics make a compromise on whether using all the correlations or completely abandoning them. To achieve the goal, we perform a screening procedure, pick up the paired covariates with strong correlations, and construct a classical Hotelling's statistic for each pair. While for the individual covariates without strong correlations with others, we apply squared t statistics to account for their respective contributions to the multivariate testing problem. As a consequence, our proposed test statistics involve a combination of the collected pairwise Hotelling's test statistics and squared t statistics. The asymptotic normality of our test statistics under the null and local alternative hypotheses are also derived under some regularity conditions. Numerical studies and two real data examples demonstrate the efficacy of our pairwise Hotelling's test. In Chapter 4, we propose a regularized t distribution and also explore its applications in multiple testing. The motivation of this topic dates back to microarray studies, where the expression levels of thousands of genes are measured simultaneously by the microarray technology. To identify genes that are differentially expressed between two or more groups, one needs to conduct hypothesis test for each gene. However, as microarray experiments are often with a small number of replicates, Student's t-tests using the sample means and standard deviations may suffer a low power for detecting differentially expressed genes. To overcome this problem, we first propose a regularized t distribution and derive its statistical properties including the probability density function and the moments. The noncentral regularized t distribution is also introduced for the power analysis. To demonstrate the usefulness of the proposed test, we apply the regularized t distribution to the gene expression detection problem. Simulation studies and two real data examples show that the regularized t-test outperforms the existing tests including Student's t-test and the Bayesian t-test in a wide range of settings, in particular when the sample size is small.
Book Synopsis Advances in Multivariate Statistical Methods by : Ashis Sengupta
Download or read book Advances in Multivariate Statistical Methods written by Ashis Sengupta and published by World Scientific. This book was released on 2009 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of research articles on multivariate statistical methods, encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. It serves as a tribute to Professor S N Roy, an eminent statistician who has made seminal contributions to the area of multivariate statistical methods, on his birth centenary. In the area of emerging applications, the topics include bioinformatics, categorical data and clinical trials, econometrics, longitudinal data analysis, microarray data analysis, sample surveys, statistical process control, etc. Researchers, professionals and advanced graduates will find the book an essential resource for modern developments in theory as well as for innovative and emerging important applications in the area of multivariate statistical methods.
Book Synopsis Some New Developments on Multiple Testing Procedures by : Lilun Du
Download or read book Some New Developments on Multiple Testing Procedures written by Lilun Du and published by . This book was released on 2015 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In chapter 2, we present a single-index modulated multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value for each hypothesis. To find the optimal rejection region for the bivariate p-value, we propose a criteria based on the ratio of probability density functions of the bivariate p-value under the true null and non-null. This criteria in the bivariate normal setting further motivates us to project the bivariate p-value to a single index p-value, for a wide range of directions. The true null distribution of the single index p-value is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Multiple testing based on chi-squared test statistics is commonly used in many scientific fields such as genomics research and brain imaging studies. However, the challenges associated with designing a formal testing procedure when there exists a general dependence structure across the chi-squared test statistics have not been well addressed. In chapter 3, we propose a Factor Connected procedure to fill in this gap. We first adopt a latent factor structure to construct a testing framework for approximating the false discovery proportion (FDP) for a large number of highly correlated chi-squared test statistics with finite degrees of freedom k. The testing framework is then connected to simultaneously testing k linear constraints in a large dimensional linear factor model involved with some observable and unobservable common factors, resulting in a consistent estimator of FDP based on the associated unadjusted p-values.
Book Synopsis A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem by : Tejas Desai
Download or read book A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem written by Tejas Desai and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: In statistics, the Behrens–Fisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an approach to the Behrens-Fisher problem. Since high-speed computers were not available in Fisher’s time, this approach was not implementable and was soon forgotten. Fortunately, now that high-speed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fisher’s approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case. In this monograph, we present the solution to the afore-mentioned multivariate generalization of the Behrens-Fisher problem. We start out by presenting a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate Behrens-Fisher problem. All methods proposed in this monograph will be include both the randomly-incomplete-data case as well as the complete-data case. Moreover, all methods considered in this monograph will be tested using both simulations and examples.
Book Synopsis Experimental Design: Procedures for the Behavioral Sciences by : Roger E. Kirk
Download or read book Experimental Design: Procedures for the Behavioral Sciences written by Roger E. Kirk and published by SAGE. This book was released on 2013 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental Design: Procedures for Behavioral Sciences, Fourth Edition is a classic text with a reputuation for accessibility and readability. It has been revised and updated to make learning design concepts even easier. Roger E. Kirk shows how three simple experimental designs can be combined to form a variety of complex designs. He provides diagrams illustrating how subjects are assigned to treatments and treatment combinations. New terms are emphasized in boldface type, there are summaries of the advantages and disadvantages of each design, and real-life examples show how the designs are used.
Book Synopsis Permutation Tests for Complex Data by : Fortunato Pesarin
Download or read book Permutation Tests for Complex Data written by Fortunato Pesarin and published by John Wiley & Sons. This book was released on 2010-02-25 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current thinking. Key Features: Examines the most up-to-date methodologies of univariate and multivariate permutation testing. Includes extensive software codes in MATLAB, R and SAS, featuring worked examples, and uses real case studies from both experimental and observational studies. Includes a standalone free software NPC Test Release 10 with a graphical interface which allows practitioners from every scientific field to easily implement almost all complex testing procedures included in the book. Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses. A supplementary website containing all of the data sets examined in the book along with ready to use software codes. Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.
Book Synopsis Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures by : Tony Cai
Download or read book Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures written by Tony Cai and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Driven by a wide range of contemporary applications, statistical inference for covariance structures has been an active area of current research in high-dimensional statistics. This review provides a selective survey of some recent developments in hypothesis testing for high-dimensional covariance structures, including global testing for the overall pattern of the covariance structures and simultaneous testing of a large collection of hypotheses on the local covariance structures with false discovery proportion and false discovery rate control. Both one-sample and two-sample settings are considered. The specific testing problems discussed include global testing for the covariance, correlation, and precision matrices, and multiple testing for the correlations, Gaussian graphical models, and differential networks.
Book Synopsis Large Scale Multiple Testing for High-Dimensional Nonparanormal Data by : Yanhui Xu
Download or read book Large Scale Multiple Testing for High-Dimensional Nonparanormal Data written by Yanhui Xu and published by . This book was released on 2019 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: False discovery control in high dimensional multiple testing has been frequently encountered in many scientific research. Under the multivariate normal distribution assumption, \cite{fan2012} proposed an approximate expression for false discovery proportion (FDP) in large-scale multiple testing when a common threshold is used and provided a consistent estimate of realized FDP when the covariance matrix is known. They further extended their study when the covariance matrix is unknown \citep{fan2017}. However, in reality, the multivariate normal assumption is often violated. In this paper, we relaxed the normal assumption by developing a testing procedure on nonparanormal distribution which extends the Gaussian family to a much larger population. The nonparanormal distribution is indeed a high dimensional Gaussian copula with nonparametric marginals. Estimating the underlying monotone functions is key to good FDP approximation. Our procedure achieved minimal mean error in approximating the FDP compared with other methods in simulation studies. We gave theoretical investigations regarding the performance of estimated covariance matrix and false rejections. In real dataset setting, our method was able to detect more differentiated genes while still maintaining the FDP under a small level. This thesis provides an important tool for approximating FDP in a given experiment where the normal assumption may not hold. We also developed a dependence-adjusted procedure which provides more power than fixed-threshold method. Our procedure also show robustness for heavy-tailed data under a variety of distributions in numeric studies.
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 Contemporary Experimental Design, Multivariate Analysis and Data Mining by : Jianqing Fan
Download or read book Contemporary Experimental Design, Multivariate Analysis and Data Mining written by Jianqing Fan and published by Springer Nature. This book was released on 2020-05-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.
Book Synopsis Innovative Statistical Methods for Public Health Data by : Ding-Geng (Din) Chen
Download or read book Innovative Statistical Methods for Public Health Data written by Ding-Geng (Din) Chen and published by Springer. This book was released on 2015-08-31 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book brings together experts working in public health and multi-disciplinary areas to present recent issues in statistical methodological development and their applications. This timely book will impact model development and data analyses of public health research across a wide spectrum of analysis. Data and software used in the studies are available for the reader to replicate the models and outcomes. The fifteen chapters range in focus from techniques for dealing with missing data with Bayesian estimation, health surveillance and population definition and implications in applied latent class analysis, to multiple comparison and meta-analysis in public health data. Researchers in biomedical and public health research will find this book to be a useful reference and it can be used in graduate level classes.
Book Synopsis Proceedings of the Pacific Rim Statistical Conference for Production Engineering by : Dongseok Choi
Download or read book Proceedings of the Pacific Rim Statistical Conference for Production Engineering written by Dongseok Choi and published by Springer. This book was released on 2018-03-27 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 2nd Pacific Rim Statistical Conference for Production Engineering: Production Engineering, Big Data and Statistics, which took place at Seoul National University in Seoul, Korea in December, 2016. The papers included discuss a wide range of statistical challenges, methods and applications for big data in production engineering, and introduce recent advances in relevant statistical methods.
Book Synopsis Multiple Comparisons and Multiple Tests Using SAS, Second Edition by : Peter H. Westfall
Download or read book Multiple Comparisons and Multiple Tests Using SAS, Second Edition written by Peter H. Westfall and published by SAS Institute. This book was released on 2011 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and extensively updated for SAS 9 and later, this work provides cutting-edge methods, specialized macros, and proven best bet procedures. The book also discusses the pitfalls and advantages of various methods, thereby helping readers to decide which is the most appropriate for their purposes. 644 pp. Pub. 7/11.
Book Synopsis Multiple Testing Procedures with Applications to Genomics by : Sandrine Dudoit
Download or read book Multiple Testing Procedures with Applications to Genomics written by Sandrine Dudoit and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. These are applied to a range of problems in biomedical and genomic research, including identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments; tests of association between gene expression measures and biological annotation metadata; sequence analysis; and genetic mapping of complex traits using single nucleotide polymorphisms. The procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions, null hypotheses, and test statistics.
Book Synopsis Analysis for Science, Engineering and Beyond by : Kalle Åström
Download or read book Analysis for Science, Engineering and Beyond written by Kalle Åström and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation. This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences. Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research. A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematics research and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology, where not only the mathematical sciences have played a role. This book will serve as a source of inspiration for a broad spectrum of researchers and research students.
Book Synopsis Acta Et Commentationes Universitatis Tartuensis de Mathematica by :
Download or read book Acta Et Commentationes Universitatis Tartuensis de Mathematica written by and published by . This book was released on 2004 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical analysis of multi-cell recordings: linking population coding models to experimental data by : Matthias Bethge
Download or read book Statistical analysis of multi-cell recordings: linking population coding models to experimental data written by Matthias Bethge and published by Frontiers E-books. This book was released on 2012-01-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern recording techniques such as multi-electrode arrays and 2-photon imaging are capable of simultaneously monitoring the activity of large neuronal ensembles at single cell resolution. This makes it possible to study the dynamics of neural populations of considerable size, and to gain insights into their computations and functional organization. The key challenge with multi-electrode recordings is their high-dimensional nature. Understanding this kind of data requires powerful statistical techniques for capturing the structure of the neural population responses and their relation with external stimuli or behavioral observations. Contributions to this Research Topic should advance statistical modeling of neural populations. Questions of particular interest include: 1. What classes of statistical methods are most useful for modeling population activity? 2. What are the main limitations of current approaches, and what can be done to overcome them? 3. How can statistical methods be used to empirically test existing models of (probabilistic) population coding? 4. What role can statistical methods play in formulating novel hypotheses about the principles of information processing in neural populations? This Research Topic is connected to a one day workshop at the Computational Neuroscience Meeting 2009 in Berlin (http://www.cnsorg.org/2009/workshops.shtml and http://www.kyb.tuebingen.mpg.de/bethge/workshops/cns2009/)
