Download or read book Statistical Inference for High Dimensional Models written by Shijie Cui and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical inference under high dimensional modelings has attracted much attention due to its wide applications in many fields. In this dissertation, I propose new methods for statistical inference in high dimensional models from three aspects: inference in high dimensional semiparametric models, inference in high dimensional matrix-valued data, and inference in high dimensional measurement error misspecified models. The first project studied statistical inference in high dimensional partially linear single index models. Firstly a profile partial penalized least squares estimator for parameter estimates for the model is proposed, and its asymptotic properties are given. Then an F-type test statistic for testing the parametric components is proposed, and its theoretical properties are established. I then propose a new test for the specification testing problem of the nonparametric components. Finally, simulation studies and empirical analysis of a real-world data set are conducted to illustrate the performance of the proposed testing procedure. The second project proposes new testing procedures in high dimensional matrix-valued data. Rank is an essential attribute for a matrix. A new type of statistic is proposed, which can make inferences on the rank of the matrix-valued data. I firstly give the theoretical property of its oracle version. To overcome the problem of empirical error accumulation, a new type of sparse SVD method is proposed, and its theoretical properties are given. Based on the newly proposed sparse SVD method, I provide a sample version statistic. Theoretical properties of this sample version statistic are given. Simulation studies and two applications to surveillance video data are provided to illustrate the performance of our newly proposed method. The third project proposes a new testing method in misspecified measurement error models. The testing method can work when there is potential model misspecification and measurement error in the model. Firstly its property is studied under the low dimensional setting. Then I develop it to the high dimensional setting. Further, I propose a method that can be adaptive to the sparsity level of the true parameters under the high dimensional setting. Simulation studies and one application to a clinical trial data set are given.
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 Statistics for High Dimensional Data written by Peter Bühlmann and published by Springer Science & Business Media. This book was released on 2011-06-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.
Download or read book Statistical Inference in High dimensional Models written by Ruben Michaël L. Dezeure and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Inference for High Dimensional Linear Models written by Zijian Guo and published by . This book was released on 2017 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional linear models play an important role in the analysis of modern data sets. Although the estimation problem has been well understood, there is still a paucity of methods and theories on the inference problem for high-dimensional linear models. This thesis focuses on statistical inference for high-dimensional linear models and consists of the following three parts. 1. The first part of the thesis considers confidence intervals for linear functionals in high-dimensional linear regression. We first establish the convergence rates of the minimax expected length for confidence intervals. Furthermore, we investigate the problem of adaptation to sparsity for the construction of confidence intervals and identify the regimes in which it is possible to construct adaptive confidence intervals. 2. In the second part of the thesis, we consider point and interval estimation of the lq loss of a given estimator in high-dimensional linear regression. For the class of rate-optimal estimators, we establish the minimax rates for estimating their lq losses, the minimax expected length of confidence intervals for their lq losses and the possibility of adaptivity of confidence intervals for their lq losses. 3. In the third part of the thesis, we consider the problem in the framework of high-dimensional instrumental variable regression and construct confidence intervals for the treatment effect in the presence of possibly invalid instrumental variables. We develop a novel selection procedure, Two-Stage Hard Thresholding (TSHT) to select valid instrumental variables and construct honest confidence intervals for the treatment effect using the selected instrumental variables.
Download or read book High Dimensional Statistics written by Martin J. Wainwright and published by Cambridge University Press. This book was released on 2019-02-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Download or read book Fundamentals of High Dimensional Statistics written by Johannes Lederer and published by Springer Nature. This book was released on 2021-11-16 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. Each chapter is complemented by numerous exercises, many of them with detailed solutions, and computer labs in R that convey valuable practical insights. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading. Given its scope, the textbook is intended for beginning graduate and advanced undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally useful to a broader audience.
Download or read book Statistical Inference in High Dimensional Linear and AFT Models written by Hao Chai and published by . This book was released on 2014 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection procedures for high dimensional data have been proposed and studied by a large amount of literature in the last few years. Most of the previous research focuses on the selection properties as well as the point estimation properties. In this paper, our goal is to construct the confidence intervals for some low-dimensional parameters in the high-dimensional setting. The models we study are the partially penalized linear and accelerated failure time models in the high-dimensional setting. In our model setup, all variables are split into two groups. The first group consists of a relatively small number of variables that are more interesting. The second group consists of a large amount of variables that can be potentially correlated with the response variable. We propose an approach that selects the variables from the second group and produces confidence intervals for the parameters in the first group. We show the sign consistency of the selection procedure and give a bound on the estimation error. Based on this result, we provide the sufficient conditions for the asymptotic normality of the low-dimensional parameters. The high-dimensional selection consistency and the low-dimensional asymptotic normality are developed for both linear and AFT models with high-dimensional data.
Download or read book Statistical Analysis for High Dimensional Data written by Arnoldo Frigessi and published by Springer. This book was released on 2016-02-16 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.
Download or read book Statistical Inference in High dimensional Matrix Models written by Matthias Löffler and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to High Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2021-08-25 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
Download or read book Statistical Inference in High dimensional Regression Models with Applications in Genome wide Association Studies written by and published by . This book was released on 2017 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Inference for High dimensional Nonparametric Models written by Jie Li and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Download or read book Mathematical Foundations of Infinite Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Download or read book Inference on Structural Changes in High Dimensional Linear Regression Models written by Hongjin Zhang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is dedicated to studying the problem of constructing asymptotically valid confidence intervals for change points in high-dimensional linear models, where the number of parameters may vastly exceed the sampling period.In Chapter 2, we develop an algorithmic estimator for a single change point and establish the optimal rate of estimation, Op(Îl 8́22 ), where Îl represents the jump size under a high dimensional scaling. The optimal result ensures the existence of limiting distributions. Asymptotic distributions are derived under both vanishing and non-vanishing regimes of jump size. In the former case, it corresponds to the argmax of a two-sided Brownian motion, while in the latter case to the argmax of a two-sided random walk, both with negative drifts. We also provide the relationship between the two distributions, which allows construction of regime (vanishing vs non-vanishing) adaptive confidence intervals.In Chapter 3, we extend our analysis to the statistical inference for multiple change points in high-dimensional linear regression models. We develop locally refitted estimators and evaluate their convergence rates both component-wise and simultaneously. Following similar manner as in Chapter 2, we achieve an optimal rate of estimation under the component-wise scenario, which guarantees the existence of limiting distributions. While we also establish the simultaneous rate which is the sharpest available by a logarithmic factor. Component-wise and joint limiting distributions are derived under vanishing and non-vanishing regimes of jump sizes, demonstrating the relationship between distributions in the two regimes.Lastly in Chapter 4, we introduce a novel implementation method for finding preliminary change points estimates via integer linear programming, which has not yet been explored in the current literature.Overall, this dissertation provides a comprehensive framework for inference on single and multiple change points in high-dimensional linear models, offering novel and efficient algorithms with strong theoretical guarantees. All theoretical results are supported by Monte Carlo simulations.
