Download or read book Semiparametric Estimation Approaches for Variant Dimension Reduction Models written by 黃名鉞 and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dimension Reduction in Statistical Modeling written by Linquan Ma (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the data object is described by a large number of features, it is often beneficial to reduce the dimension of the data, so that the statistical analysis can have better efficiencies. Recently, a new dimension reduction method called the envelope method by Cook, Li, and Chiaromonte (2010) has been proposed in multivariate regressions. It has the potential to gain substantial efficiency over the standard least squares estimator. Chapter 2 proposes an approach to use the envelope method when the predictors and/or the responses are missing at random. When there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. We incorporate the envelope structure in the expectation-maximization (EM) algorithm. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. We give asymptotic properties of our method under both normal and non-normal cases. Chapter 3 extends the envelope model to the mixed effects model for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Chapter 4 proposes a semiparametric variant of the inner envelope model (Su and Cook, 2012) that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. The instrumental variables (IV) are frequently used in observational studies to recover the effect of exposure in the presence of unmeasured confounding. A key fact is that the strength of IV matters: an IV with a stronger association with the exposure results in a more accurate estimation of a causal effect. While it is hard to find a stronger IV, we generalize a sufficient dimension method to remove immaterial IVs. Chapter 5 investigates two different ways of incorporating the envelope method into IV regression. We show that the first stage envelope method does not yield any efficiency gain on the standard IV estimator, however, it may reduce the finite sample bias. The second stage envelope can achieve substantial efficiency gain under certain conditions.

Download or read book Dimension Reduction in Statistical Modeling written by Linquan Ma (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the data object is described by a large number of features, it is often beneficial to reduce the dimension of the data, so that the statistical analysis can have better efficiencies. Recently, a new dimension reduction method called the envelope method by Cook, Li, and Chiaromonte (2010) has been proposed in multivariate regressions. It has the potential to gain substantial efficiency over the standard least squares estimator. Chapter 2 proposes an approach to use the envelope method when the predictors and/or the responses are missing at random. When there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. We incorporate the envelope structure in the expectation-maximization (EM) algorithm. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. We give asymptotic properties of our method under both normal and non-normal cases. Chapter 3 extends the envelope model to the mixed effects model for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Chapter 4 proposes a semiparametric variant of the inner envelope model (Su and Cook, 2012) that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. The instrumental variables (IV) are frequently used in observational studies to recover the effect of exposure in the presence of unmeasured confounding. A key fact is that the strength of IV matters: an IV with a stronger association with the exposure results in a more accurate estimation of a causal effect. While it is hard to find a stronger IV, we generalize a sufficient dimension method to remove immaterial IVs. Chapter 5 investigates two different ways of incorporating the envelope method into IV regression. We show that the first stage envelope method does not yield any efficiency gain on the standard IV estimator, however, it may reduce the finite sample bias. The second stage envelope can achieve substantial efficiency gain under certain conditions.

Download or read book Semi parametric Exponential Family PCA written by Sajama Sajama and published by . This book was released on 2004 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal component analysis is a widely used technique for dimensionality reduction, but is not based on a probability model. Many recently proposed dimension reduction methods are based on latent variable modelling with restrictive assumptions on the latent distribution. We present a semi-parametric latent variable model based technique for density modelling, dimensionality reduction and visualization. Unlike previous methods, we estimate the latent distribution non-parametrically. Using this estimated prior to reduce dimensions ensures that multi-modality is better preserved in the projected space. In addition, we allow the components of latent variable models to be drawn from the exponential family which makes the method suitable for special data types, for example binary or count data. We discuss connections to other probabilistic and non-probabilistic dimension reduction schemes based on gaussian and other exponential family distributions. Simulations on real valued, binary and count data show favorable comparison to other related schemes both in terms of separating different populations and generalization to unseen samples.

Download or read book Semiparametric Modeling of Implied Volatility written by Matthias R. Fengler and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.

Download or read book Semiparametric Estimation of Selectivity Models written by Markus Frölich and published by . This book was released on 2002 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semiparametric Approaches to Dimension Reduction written by and published by . This book was released on 1992 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Statistics in Precision Health written by Yichuan Zhao and published by Springer Nature. This book was released on with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantile Regression written by Roger Koenker and published by Cambridge University Press. This book was released on 2005-05-05 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Download or read book A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables written by Jia Chen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Semiparametric Estimation Methods for Nonlinear Panel Data Models and Mismeasured Dependent Variables written by Jason Abrevaya and published by . This book was released on 1996 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 462 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 Efficient Estimation and Order Determination for Sufficient Dimension Reduction written by Wei Luo and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction (SDR) has driven intense interest in the recent decades as a solution to deal with high-dimensional data. The goal of SDR is to construct, usually by a linear transformation of the original predictor, a lower-dimensional sufficient statistic that serves as the new predictor in subsequent modeling. An important problem in SDR, is to determine the reduced dimension of the new predictor. In this dissertation, we first propose two order-determination methods that are applicable to a large class of SDR methods, with both of them proved consistent and shown efficient via simulation study and real data examples.Another part of the dissertation focuses on the development of a new class of efficient estimators of the linear transformation under various SDR assumptions, in a unifying semi-parametric approach. These estimators are expected to outperform their competitors in the literature, which were developed without consideration of semi-parametric efficiency. We derive the efficient score functions that generate these estimators, together with a computationally efficient algorithm. We also conduct the corresponding simulation studies and real data analysis to further show the effectiveness of the estimators in application.

Download or read book Static Analysis written by Agostino Cortesi and published by Springer Science & Business Media. This book was released on 1999-09-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Static analysis is increasingly recognized as a fundamental reasearch area aimed at studying and developing tools for high performance implementations and v- i cation systems for all programming language paradigms. The last two decades have witnessed substantial developments in this eld, ranging from theoretical frameworks to design, implementation, and application of analyzers in optim- ing compilers. Since 1994, SAS has been the annual conference and forum for researchers in all aspects of static analysis. This volume contains the proceedings of the 6th International Symposium on Static Analysis (SAS’99) which was held in Venice, Italy, on 22{24 September 1999. The previous SAS conferences were held in Namur (Belgium), Glasgow (UK), Aachen (Germany), Paris (France), and Pisa (Italy). The program committee selected 18 papers out of 42 submissions on the basis of at least three reviews. The resulting volume o ers to the reader a complete landscape of the research in this area. The papers contribute to the following topics: foundations of static analysis, abstract domain design, and applications of static analysis to di erent programming paradigms (concurrent, synchronous, imperative, object oriented, logical, and functional). In particular, several papers use static analysis for obtaining state space reduction in concurrent systems. New application elds are also addressed, such as the problems of security and secrecy.

Download or read book Nonlinear Statistical Modeling written by Takeshi Amemiya and published by Cambridge University Press. This book was released on 2001-01-08 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection investigates parametric, semiparametric, nonparametric, and nonlinear estimation techniques in statistical modeling.

Download or read book The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics written by Jeffrey Racine and published by Oxford University Press. This book was released on 2014-04 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures.

Download or read book Encyclopedia of Statistical Sciences Volume 3 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES