Download or read book Application of Influence Function in Sufficient Dimension Reduction Models written by Prabha Shrestha and published by . This book was released on 2020 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In regression analysis, sufficient dimension reduction (SDR) models have gained significant popularity in the past three decades. While many methods have been proposed in the literature regarding the analysis of SDR models, the vast majority are of the type called inverse regression methods, pioneered by the sliced inverse regression method (Li \cite{Li91}). Most of these inverse regression methods rely on a matrix, commonly known as the central matrix. One of the main goals of the analysis of SDR models is the estimation of the central space. An influence function (IF) is a tool that analyzes the performance of a statistical estimator. In this dissertation, we focus on the application of IF on the analysis of SDR models. There are various inverse regression methods in existence. But none of them stands out in all cases, and it is not clear which central matrix one should use out of numerous options existing in the literature. We propose an IF-based approach for selection of a best performing central matrix from a class of inverse regression methods, and we extend this approach to the situation where the data are partially contaminated. Asymptotic results are established, and an extensive simulation study is conducted to examine the performance of the proposed algorithm. Another issue in an SDR model is the estimation of the dimension of its central space. Based on the IF, we propose a measure that combines the eigenvalues of the central matrix and an IF measure to estimate the dimension of the central space. In addition, we analyze the IF of the functional of Benasseni's measure for a specific inverse regression method, the $k{\text-th}$ moment method.

Download or read book Analysis of Sparse Sufficient Dimension Reduction Models written by Yeshan Withanage and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction (SDR) in regression analysis with response variable y and predictor vector x is focused on reducing the dimension of x to a small number of linear combinations of the components in x. Since the introduction of the inverse regression method, SDR became a very active topic in the literature. When the dimension p of x is increasing with the number of observations n, the traditional SDR methods may not perform well. The purpose of this study is two fold, theoretical and empirical. In the theoretical analysis, I provide a proof for the consistency of a variable selection procedure in sparse single-index models (a special SDR model) through an inverse regression method called CUME. And for the case of multiple linear regression, I obtain the influence functions for estimators of the parameter vector with SCAD and MCP penalties by extending the idea of LASSO influence function. In the empirical aspect, I combine the LASSO-SIR algorithm with the influence function of LASSO to construct a new metric for choosing the penalty parameter for variable selection as an alternative approach to the usual cross-validation method. From the empirical analysis, it was found that the newly proposed influence function-based measure outperforms the traditional cross-validation method in a wide range of settings. Finally, I also propose an algorithm to estimate the structural dimension d of SDR models with large dimension p

Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.

Download or read book Dimension Reduction and Sufficient Graphical Models written by Kyongwon Kim and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods I develop in my thesis are based on linear or nonlinear sufficient dimension reduction. The basic principle of linear sufficient dimension reduction is to extract a small number of linear combinations of predictor variables, which can represent original predictor variables without loss of information on the conditional distribution of response variable given predictor variables. Nonlinear sufficient dimension reduction is a more generalized version of linear sufficient dimension reduction to the nonlinear context. I am focusing on applying sufficient dimension reduction methods into two areas, regression modeling and graphical models. The first project is about statistical inference in regression context after sufficient dimension reduction. Second, I apply nonlinear sufficient dimension reduction method to the well known statistical graphical models in machine learning. These projects have consistency in a context that discovering areas that sufficient dimension reduction can be applied and establishing statistical theory behind their applications. My first project is about post sufficient dimension reduction statistical inference. The methodologies of sufficient dimension reduction have undergone extensive developments in the past three decades. However, there has been a lack of systematic and rigorous development of post dimension reduction inference, which has seriously hindered its applications. The current common practice is to treat the estimated sufficient predictors as the true predictors and use them as the starting point of the downstream statistical inference. However, this naive inference approach would grossly overestimate the confidence level of an interval, or the power of a test, leading to the distorted results. In this project, we develop a general and comprehensive framework of post dimension reduction inference, which can accommodate any dimension reduction method and model building method, as long as their corresponding influence functions are available. Within this general framework, we derive the influence functions and present the explicit post reduction formulas for the combinations of numerous dimension reduction and model building methods. We then develop post reduction inference methods for both confidence interval and hypothesis testing. We investigate the finite-sample performance of our procedures by simulations and a real data analysis. My second project is about applying nonlinear dimension reduction technique to graphical models. We introduce the Sufficient Graphical Model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. Graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize a conditional independence, our graphical model is based on a conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way, we avoid the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.

Download or read book Statistical Causal Inferences and Their Applications in Public Health Research written by Hua He and published by Springer. This book was released on 2016-10-26 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles and presents new developments in statistical causal inference. The accompanying data and computer programs are publicly available so readers may replicate the model development and data analysis presented in each chapter. In this way, methodology is taught so that readers may implement it directly. The book brings together experts engaged in causal inference research to present and discuss recent issues in causal inference methodological development. This is also a timely look at causal inference applied to scenarios that range from clinical trials to mediation and public health research more broadly. In an academic setting, this book will serve as a reference and guide to a course in causal inference at the graduate level (Master's or Doctorate). It is particularly relevant for students pursuing degrees in statistics, biostatistics, and computational biology. Researchers and data analysts in public health and biomedical research will also find this book to be an important reference.

Download or read book Selected Water Resources Abstracts written by and published by . This book was released on 1986 with total page 1140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Springer Handbook of Engineering Statistics written by Hoang Pham and published by Springer Nature. This book was released on 2023-04-20 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In today’s global and highly competitive environment, continuous improvement in the processes and products of any field of engineering is essential for survival. This book gathers together the full range of statistical techniques required by engineers from all fields. It will assist them to gain sensible statistical feedback on how their processes or products are functioning and to give them realistic predictions of how these could be improved. The handbook will be essential reading for all engineers and engineering-connected managers who are serious about keeping their methods and products at the cutting edge of quality and competitiveness.

Download or read book On Analysis of Sufficient Dimension Reduction Models written by Panduan An and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Developments of Dimension Reduction written by Lei Huo and published by . This book was released on 2018 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Variable selection becomes more crucial than before, since high dimensional data are frequently seen in many research areas. Many model-based variable selection methods have been developed. However, the performance might be poor when the model is mis-specified. Sufficient dimension reduction (SDR, Li 1991; Cook 1998) provides a general framework for model-free variable selection methods. In this thesis, we first propose a novel model-free variable selection method to deal with multi-population data by incorporating the grouping information. Theoretical properties of our proposed method are also presented. Simulation studies show that our new method significantly improves the selection performance compared with those ignoring the grouping information. In the second part of this dissertation, we apply partial SDR method to conduct conditional model-free variable (feature) screening for ultra-high dimensional data, when researchers have prior information regarding the importance of certain predictors based on experience or previous investigations. Comparing to the state of art conditional screening method, conditional sure independence screening (CSIS; Barut, Fan and Verhasselt, 2016), our method greatly outperforms CSIS for nonlinear models. The sure screening consistency property of our proposed method is also established"--Abstract, page iv.

Download or read book Dimension Reduced Modeling of Blood Flow in Large Arteries written by Tobias Köppl and published by Springer Nature. This book was released on 2023-07-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains an in-depth and coherent treatment of dimension-reduced modeling of blood flows on the level of large vessels (macrocirculation). The authors reduce the complexity by combining a one-dimensional Navier-Stokes equation and a simplified FSI-concept. The influence of omitted vessels, which are subsequent to the outlets of larger vessels, is accounted for by systems of ordinary differential equations (0D models). The target audience primarily comprises research experts in the field of biomedical engineering, but the book may also be beneficial for graduate students alike.

Download or read book A Simulation Study on Using Moment Functions for Sufficient Dimension Reduction written by Lipu Tian and published by . This book was released on 2012 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transforms in Sufficient Dimension Reduction and Their Applications in High Dimensional Data written by Jiaying Weng and published by . This book was released on 2019 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Influence Function Considerations for Principal Component Analysis written by Lindsey Kevan and published by . This book was released on 2006 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this thesis is to study Principal Component Analysis (PCA) via the influence function. PCA is often used to reduce the complexity of high dimensional datasets by finding lower order projections that explain much of the variability within the data. However, many statistical estimators such as PCA that are applied to such data can be highly influenced by just a few observations. The influence function is a useful diagnostic tool that can assist in determining influential observation types on statistical estimators. We study the influence functions with respect to individual and multiple principal components and show how these may be used to highlight the types of observations that may or may not be influential in practice. It is also common in statistical practice to study the effects of outlying observations. However, not all outliers are influential in estimation and likewise not all influential observations are outliers. We therefore give consideration to the use of sample versions of the influential functions that may be used to detect influential observations in practice as opposed to employing classical outlier detection methods.

Download or read book Converter Applications and their Influence on Large Electrical Machines written by Oliver Drubel and published by Springer Science & Business Media. This book was released on 2013-01-26 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Converter driven applications are applied in more and more processes. Almost any installed wind-farm, ship drives, steel mills, several boiler feed water pumps, extruder and many other applications operate much more efficient and economic in case of variable speed solutions. The boundary conditions for a motor or generator will change, if it is supplied by a converter. An electrical machine, which is operated by a converter, can no longer be regarded as an independent component, but is embedded in a system consisting of converter and machine. This book gives an overview of existing converter designs for large electrical machines. Methods for the appropriate calculation of machine phenomena, which are implied by converters are derived in the power range above 500kVA. It is shown how due to the converter inherent higher voltage harmonics and pulse frequencies special phenomena are caused inside the machine which can be the reason for malfunction. It is demonstrated that additional losses create additional temperature increases or voltage peaks. The book describes how torque ripple can occur, which endanger the mechanical shaft system and last but not least shaft voltages are induced, which are sometimes sufficient in amplitude to damage bearings or to disturb sensors of the protection arrangements.

Download or read book Dissipative Quantum Mechanics of Nanostructures written by Andrei D. Zaikin and published by CRC Press. This book was released on 2019-05-24 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing miniaturization of electronic devices, together with the quickly growing number of nanotechnological applications, demands a profound understanding of the underlying physics. Most of the fundamental problems of modern condensed matter physics involve various aspects of quantum transport and fluctuation phenomena at the nanoscale. In nanostructures, electrons are usually confined to a limited volume and interact with each other and lattice ions, simultaneously suffering multiple scattering events on impurities, barriers, surface imperfections, and other defects. Electron interaction with other degrees of freedom generally yields two major consequences, quantum dissipation and quantum decoherence. In other words, electrons can lose their energy and ability for quantum interference even at very low temperatures. These two different, but related, processes are at the heart of all quantum phenomena discussed in this book. This book presents copious details to facilitate the understanding of the basic physics behind a result and the learning to technically reproduce the result without delving into extra literature. The book subtly balances the description of theoretical methods and techniques and the display of the rich landscape of the physical phenomena that can be accessed by these methods. It is useful for a broad readership ranging from master’s and PhD students to postdocs and senior researchers.

Download or read book Exploration of a Nonlinear World written by Kung-sik Chan and published by World Scientific. This book was released on 2009 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensions of Howell Tong's threshold approach to other fields of statistics abound. This volume is dedicated to his 65th birthday and consists of in-depth contributions from leading experts in a variety of fields of statistics, ecology, economics and finance as well as some of Tong's reprints.

Download or read book Matrix Methods Theory Algorithms And Applications Dedicated To The Memory Of Gene Golub written by Vadim Olshevsky and published by World Scientific. This book was released on 2010-04-05 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.