Download or read book Bootstrap Based Hypothesis Testing for High dimensional Data written by Nilanjan Chakraborty and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades inference problems on high-dimensional data that arise in finance, genetics and information technology have gained huge momentum. In this work, the main focus will be on developing bootstrap testing procedures under high dimensional set up for the following two hypotheses testing problems.i)High-dimensional Multivariate Analysis of Variance ii)Testing the equality of two covariance matrices in the two sample set up.The statistics considered for testing are infinity norm based statistics over either weighted sums or differences across various samples. We provide Gaussian approximation results for normalized sums of high dimensional random vectors and U-statistics under some weak conditions on moments and tails of their marginal distributions. The obtained results are free from the assumption of sparsity and correlation structures among the components of the random vectors. For the implementation of these tests, we develop multiplier bootstrap and jackknifed multiplier bootstrap procedures. These newly developed bootstrap techniques ensure first order accuracy of the asymptotic level and power of the formulated tests, enhancing their applicability. We also provide consistency of the proposed test against both fixed and local alternatives.

Download or read book High Dimensional Data Bootstrap written by Victor Chernozhukov and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of high-dimensional bootstrap: construction of simultaneous confidence sets for high-dimensional vector parameters, multiple hypothesis testing via step-down, postselection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions.

Download or read book Statistical Inference from High Dimensional Data written by Carlos Fernandez-Lozano and published by MDPI. This book was released on 2021-04-28 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Real-world problems can be high-dimensional, complex, and noisy • More data does not imply more information • Different approaches deal with the so-called curse of dimensionality to reduce irrelevant information • A process with multidimensional information is not necessarily easy to interpret nor process • In some real-world applications, the number of elements of a class is clearly lower than the other. The models tend to assume that the importance of the analysis belongs to the majority class and this is not usually the truth • The analysis of complex diseases such as cancer are focused on more-than-one dimensional omic data • The increasing amount of data thanks to the reduction of cost of the high-throughput experiments opens up a new era for integrative data-driven approaches • Entropy-based approaches are of interest to reduce the dimensionality of high-dimensional data

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.

Download or read book Bootstraptests in Linear Models with Many Regressors written by Patrick Richard and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with bootstrap hypothesis testing in high dimensional linear regression models. Using a theoretical framework recently introduced by Anatolyev (2012), we show that bootstrap F, LR and LM tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size. These results are derived for models with iid error terms, but Monte Carlo evidence suggests that they extend to the wild bootstrap in the presence of heteroskedasticity and to bootstrap methods for heavy tailed data.

Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Academic Press. This book was released on 2021-09-18 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Robust Estimating and Hypothesis Testing, Fifth Edition is a useful ‘how-to’ on the application of robust methods utilizing easy-to-use software. This trusted resource provides an overview of modern robust methods, including improved techniques for dealing with outliers, skewed distribution curvature, and heteroscedasticity that can provide substantial gains in power. Coverage includes techniques for comparing groups and measuring effect size, current methods for comparing quantiles, and expanded regression methods for both parametric and nonparametric techniques. The practical importance of these varied methods is illustrated using data from real world studies. Over 1700 R functions are included to support comprehension and practice. Includes the latest developments in robust regression Provides many new, improved and accessible R functions Offers comprehensive coverage of ANOVA and ANCOVA methods

Download or read book Hypothesis Testing of High Dimensional Data with Applications to Medical Image Analysis written by Kun Nie and published by . This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hypothesis Testing with High dimensional Data written by Sen Zhao and published by . This book was released on 2017 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past two decades, vast high-dimensional biomedical datasets have become mainstay in various biomedical applications from genomics to neuroscience. These high-dimensional data enable researchers to answer scientific questions that are impossible to answer with classical, low-dimensional datasets. However, due to the "curse of dimensionality", such high-dimensional datasets also pose serious statistical challenges. Motivated by these emerging applications, statisticians have devoted much effort to developing estimation methods for high-dimensional linear models and graphical models. However, there is still little progress on quantifying the uncertainty of the estimates, e.g., obtaining p-values and confidence intervals, which are crucial for drawing scientific conclusions. While encouraging advances have been made in this area over the past couple of years, the majority of existing high-dimensional hypothesis testing methods still suffer from low statistical power or high computational intensity. In this dissertation, we focus on developing hypothesis testing methods for high-dimensional linear and graphical models. In Chapter 2, we investigate a naive and simple two-step hypothesis testing procedure for linear models. We show that, under appropriate conditions, such a simple procedure controls type-I error rate, and is closely connected to more complicated alternatives. We also show in numerical studies that such a simple procedure achieves similar performance as procedures that are computationally more intense. In Chapter 3, we consider hypothesis testing for linear regression that incorporates external information about the relationship between variables represented by a graph, such as the gene regulatory network. We show in theory and numerical studies that by incorporating informative external information, our proposal is substantially more powerful than existing methods that ignore such information. We also propose a more robust procedure for settings where the external information is potentially inaccurate or imprecise. This robust procedure could adaptively choose the amount of external information to be incorporated based on the data. In Chapter 4, we shift our focus to Gaussian graphical models. We propose a novel procedure to test whether two Gaussian graphical models share the same edge set, while controlling the false positive rate. In the case that two networks are different, our proposals could identify specific nodes and edges that show differential connectivity. In this chapter, we also demonstrate that when the goal is to identify differentially connected nodes and edges, the results from our proposal are more interpretable than existing procedures based on covariance or precision matrices. We finish the dissertation with a discussion in Chapter 5, in which we present viable future research directions, and discuss a possible extension of our proposals to vector autoregression models for time series.

Download or read book Use of Bootstrapping in Hypothesis Testing written by Md. Siddikur Rahman and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The bootstrap is a resampling method for statistical inference, which helps us in most cases, to increase the degree of trust that can be placed in a result based on limited sample of data. When the sample size is small and their EDF is unknown, the bootstrap method is used to make asymptotically normal or near normal. Bootstrap confidence interval thus has double potential advantages over most statistical technique-due to the fact that, it is confidence interval and due to the fact that it is based on bootstrap method. There are several methods of bootstrap confidence interval: the standard method, bootstrap-t, the percentile, the Bias Corrected and Accelerated (BCa) and the approximate bootstrap confidence interval. Among the methods, the BCa method gives us better result with respect to the properties- length, shape and symmetry. ABC method also gives good result in some cases. The bootstrap-t and percentile methods have the identical and close result. The shape of percentile method, in most cases, is good but its forced symmetry makes it poor.In hypothesis testing, bootstrap approach performs better than the classical approach in terms of power.

Download or read book High Dimensional Data Analysis in Cancer Research written by Xiaochun Li and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate analysis is a mainstay of statistical tools in the analysis of biomedical data. It concerns with associating data matrices of n rows by p columns, with rows representing samples (or patients) and columns attributes of samples, to some response variables, e.g., patients outcome. Classically, the sample size n is much larger than p, the number of variables. The properties of statistical models have been mostly discussed under the assumption of fixed p and infinite n. The advance of biological sciences and technologies has revolutionized the process of investigations of cancer. The biomedical data collection has become more automatic and more extensive. We are in the era of p as a large fraction of n, and even much larger than n. Take proteomics as an example. Although proteomic techniques have been researched and developed for many decades to identify proteins or peptides uniquely associated with a given disease state, until recently this has been mostly a laborious process, carried out one protein at a time. The advent of high throughput proteome-wide technologies such as liquid chromatography-tandem mass spectroscopy make it possible to generate proteomic signatures that facilitate rapid development of new strategies for proteomics-based detection of disease. This poses new challenges and calls for scalable solutions to the analysis of such high dimensional data. In this volume, we will present the systematic and analytical approaches and strategies from both biostatistics and bioinformatics to the analysis of correlated and high-dimensional data.

Download or read book Permutation Tests written by Phillip Good and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step guide to the application of permutation tests in biology, medicine, science, and engineering. The intuitive and informal style makes this manual ideally suitable for students and researchers approaching these methods for the first time. In particular, it shows how to handle the problems of missing and censored data, nonresponders, after-the-fact covariates, and outliers.

Download or read book Bootstrap based Hypothesis Testing written by James Samuel Allison and published by . This book was released on 2008 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Perspectives on Big Data Analysis written by S. Ejaz Ahmed and published by American Mathematical Society. This book was released on 2014-08-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Perspectives on High-dimensional Data Analysis II, held May 30-June 1, 2012, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. This book collates applications and methodological developments in high-dimensional statistics dealing with interesting and challenging problems concerning the analysis of complex, high-dimensional data with a focus on model selection and data reduction. The chapters contained in this book deal with submodel selection and parameter estimation for an array of interesting models. The book also presents some surprising results on high-dimensional data analysis, especially when signals cannot be effectively separated from the noise, it provides a critical assessment of penalty estimation when the model may not be sparse, and it suggests alternative estimation strategies. Readers can apply the suggested methodologies to a host of applications and also can extend these methodologies in a variety of directions. This volume conveys some of the surprises, puzzles and success stories in big data analysis and related fields. This book is co-published with the Centre de Recherches Mathématiques.

Download or read book High Dimensional Probability II written by Evarist Giné and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.

Download or read book Handbook of Big Data Analytics written by Wolfgang Karl Härdle and published by Springer. This book was released on 2018-07-20 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing a broad range of big data analytics in cross-disciplinary applications, this essential handbook focuses on the statistical prospects offered by recent developments in this field. To do so, it covers statistical methods for high-dimensional problems, algorithmic designs, computation tools, analysis flows and the software-hardware co-designs that are needed to support insightful discoveries from big data. The book is primarily intended for statisticians, computer experts, engineers and application developers interested in using big data analytics with statistics. Readers should have a solid background in statistics and computer science.

Download or read book Bootstraptests in Linear Models with Many Regressors written by and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with bootstrap hypothesis testing in high dimensional linear regression models. Using a theoretical framework recently introduced by Anatolyev (2012), we show that bootstrap F, LR and LM tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size. These results are derived for models with iid error terms, but Monte Carlo evidence suggests that they extend to the wild bootstrap in the presence of heteroskedasticity and to bootstrap methods for heavy tailed data.

Download or read book Simulation for Data Science with R written by Matthias Templ and published by Packt Publishing Ltd. This book was released on 2016-06-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harness actionable insights from your data with computational statistics and simulations using R About This Book Learn five different simulation techniques (Monte Carlo, Discrete Event Simulation, System Dynamics, Agent-Based Modeling, and Resampling) in-depth using real-world case studies A unique book that teaches you the essential and fundamental concepts in statistical modeling and simulation Who This Book Is For This book is for users who are familiar with computational methods. If you want to learn about the advanced features of R, including the computer-intense Monte-Carlo methods as well as computational tools for statistical simulation, then this book is for you. Good knowledge of R programming is assumed/required. What You Will Learn The book aims to explore advanced R features to simulate data to extract insights from your data. Get to know the advanced features of R including high-performance computing and advanced data manipulation See random number simulation used to simulate distributions, data sets, and populations Simulate close-to-reality populations as the basis for agent-based micro-, model- and design-based simulations Applications to design statistical solutions with R for solving scientific and real world problems Comprehensive coverage of several R statistical packages like boot, simPop, VIM, data.table, dplyr, parallel, StatDA, simecol, simecolModels, deSolve and many more. In Detail Data Science with R aims to teach you how to begin performing data science tasks by taking advantage of Rs powerful ecosystem of packages. R being the most widely used programming language when used with data science can be a powerful combination to solve complexities involved with varied data sets in the real world. The book will provide a computational and methodological framework for statistical simulation to the users. Through this book, you will get in grips with the software environment R. After getting to know the background of popular methods in the area of computational statistics, you will see some applications in R to better understand the methods as well as gaining experience of working with real-world data and real-world problems. This book helps uncover the large-scale patterns in complex systems where interdependencies and variation are critical. An effective simulation is driven by data generating processes that accurately reflect real physical populations. You will learn how to plan and structure a simulation project to aid in the decision-making process as well as the presentation of results. By the end of this book, you reader will get in touch with the software environment R. After getting background on popular methods in the area, you will see applications in R to better understand the methods as well as to gain experience when working on real-world data and real-world problems. Style and approach This book takes a practical, hands-on approach to explain the statistical computing methods, gives advice on the usage of these methods, and provides computational tools to help you solve common problems in statistical simulation and computer-intense methods.