Single Index Regression Models

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Nonparametric and Semiparametric Models

Author : Wolfgang Karl Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 364217146X
Total Pages : 317 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Nonparametric and Semiparametric Models by : Wolfgang Karl Härdle

Download or read book Nonparametric and Semiparametric Models written by Wolfgang Karl Härdle and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

Single-index Regression Models

Author : Jingwei Wu
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (94 download)

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Book Synopsis Single-index Regression Models by : Jingwei Wu

Download or read book Single-index Regression Models written by Jingwei Wu and published by . This book was released on 2015 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters.

Score Tests for the Single Index Model

Author : Jeffrey S. Simonoff
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Score Tests for the Single Index Model by : Jeffrey S. Simonoff

Download or read book Score Tests for the Single Index Model written by Jeffrey S. Simonoff and published by . This book was released on 2008 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The single index model is a generalization of the linear regression model with E(y|x) = g, whereg is an unknown function. The model provides a flexible alternative to the linear regression modelwhile providing more structure than a fully nonparametric approach. Although the fitting of single indexmodels does not require distributional assumptions on the error term, the properties of the estimatesdepend on such assumptions, as does practical application of the model. In this article score testsare derived for three potential misspecifications of the single index model: heteroscedasticity in theerrors, autocorrelation in the errors, and the omission of an important variable in the linear index.These tests have a similar structure to corresponding tests for nonlinear regression models. Monte Carlosimulations demonstrate that the first two tests hold their nominal size well and have good powerproperties in identifying model violations, often outperforming other tests. Testing for the need foradditional covariates can be effective, but is more difficult. The score tests are applied to three realdatasets, demonstrating that the tests can identify important model violations that affect inference, andthat approaches that do not take model misspecifications into account can lead to very different results.

Functional and High-Dimensional Statistics and Related Fields

Author : Germán Aneiros
Publisher : Springer
ISBN 13 : 9783030477585
Total Pages : 254 pages
Book Rating : 4.4/5 (775 download)

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Book Synopsis Functional and High-Dimensional Statistics and Related Fields by : Germán Aneiros

Download or read book Functional and High-Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer. This book was released on 2021-06-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Advances in Contemporary Statistics and Econometrics

Author : Abdelaati Daouia
Publisher : Springer Nature
ISBN 13 : 3030732495
Total Pages : 713 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Advances in Contemporary Statistics and Econometrics by : Abdelaati Daouia

Download or read book Advances in Contemporary Statistics and Econometrics written by Abdelaati Daouia and published by Springer Nature. This book was released on 2021-06-14 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.

Advances in Statistical Modeling and Inference

Author : Vijay Nair
Publisher : World Scientific
ISBN 13 : 9812703691
Total Pages : 698 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Advances in Statistical Modeling and Inference by : Vijay Nair

Download or read book Advances in Statistical Modeling and Inference written by Vijay Nair and published by World Scientific. This book was released on 2007 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been major developments in the field of statistics over the last quarter century, spurred by the rapid advances in computing and data-measurement technologies. These developments have revolutionized the field and have greatly influenced research directions in theory and methodology. Increased computing power has spawned entirely new areas of research in computationally-intensive methods, allowing us to move away from narrowly applicable parametric techniques based on restrictive assumptions to much more flexible and realistic models and methods. These computational advances have also led to the extensive use of simulation and Monte Carlo techniques in statistical inference. All of these developments have, in turn, stimulated new research in theoretical statistics.This volume provides an up-to-date overview of recent advances in statistical modeling and inference. Written by renowned researchers from across the world, it discusses flexible models, semi-parametric methods and transformation models, nonparametric regression and mixture models, survival and reliability analysis, and re-sampling techniques. With its coverage of methodology and theory as well as applications, the book is an essential reference for researchers, graduate students, and practitioners.

Partially Linear Models

Author : Wolfgang Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 3642577008
Total Pages : 210 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Partially Linear Models by : Wolfgang Härdle

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.

Extensions of Semiparametric Single Index Models

Author : Chen Wang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Extensions of Semiparametric Single Index Models by : Chen Wang

Download or read book Extensions of Semiparametric Single Index Models written by Chen Wang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recent decades, researchers have made tremendous progress in the study of nonparametric and semiparametric models. Among them, the semiparametric single-index model is intensively studied due to its simplicity and flexibility. In a single-index model, conditional response mean depends on the independent covariates through a single linear combination of the covariates along with an unknown function, which is sometimes called a link function. Therefore, the single-index model relaxes some of the restrictive assumptions of familiar parametric models, such as linear models and logit models. In addition, single-index models are useful dimension reduction techniques with great estimation precision. In this dissertation, we focus on extensions of the single-index models in two directions. Chapter 2 considers estimation and variable selection problems of additive multi-index models. Without knowing significant covariates corresponding to additive components, we have automatically selected significant variables for each component. We have developed a numerically stable and computationally fast estimation procedure by utilizing both the least squares method and the local optimization. Further, we have established asymptotic normality for proposed estimators of index coefficients as well as the consistency for nonparametric function estimators. Simulation experiments have provided strong evidence that corroborates the asymptotic theory. A baseball hitters’ salary example has been used to illustrate the application of the model. Furthermore, to better explore the upper and the lower frontiers of data, we have studied the expectile regression of single-index models in Chapter 3. With the spline smoothing technique of the nonparametric regression, different levels of conditional expectile curves provide us more comprehensive information about the data structure and extreme data values. Unlike in Chapter 2, we have applied the minimax concave penalty to achieve the variable selection for expectile regression. In the numerical analysis, simulated examples as well as a clinical trial data set have been investigated.

Nonparametric Functional Data Analysis

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
ISBN 13 : 0387366202
Total Pages : 260 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Nonparametric Functional Data Analysis by : Frédéric Ferraty

Download or read book Nonparametric Functional Data Analysis written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Penalized Spline Estimation for Partially Linear Single Index Models

Author : Yan Yu
Publisher :
ISBN 13 :
Total Pages : 258 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Penalized Spline Estimation for Partially Linear Single Index Models by : Yan Yu

Download or read book Penalized Spline Estimation for Partially Linear Single Index Models written by Yan Yu and published by . This book was released on 2001 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Regression & Linear Modeling

Author : Jason W. Osborne
Publisher : SAGE Publications
ISBN 13 : 1506302750
Total Pages : 489 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Regression & Linear Modeling by : Jason W. Osborne

Download or read book Regression & Linear Modeling written by Jason W. Osborne and published by SAGE Publications. This book was released on 2016-03-24 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a conversational tone, Regression & Linear Modeling provides conceptual, user-friendly coverage of the generalized linear model (GLM). Readers will become familiar with applications of ordinary least squares (OLS) regression, binary and multinomial logistic regression, ordinal regression, Poisson regression, and loglinear models. Author Jason W. Osborne returns to certain themes throughout the text, such as testing assumptions, examining data quality, and, where appropriate, nonlinear and non-additive effects modeled within different types of linear models.

Doing Meta-Analysis with R

Author : Mathias Harrer
Publisher : CRC Press
ISBN 13 : 1000435636
Total Pages : 500 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Doing Meta-Analysis with R by : Mathias Harrer

Download or read book Doing Meta-Analysis with R written by Mathias Harrer and published by CRC Press. This book was released on 2021-09-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Meta-Analysis with R: A Hands-On Guide serves as an accessible introduction on how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including calculation and pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced but highly relevant topics such as network meta-analysis, multi-three-level meta-analyses, Bayesian meta-analysis approaches and SEM meta-analysis are also covered. A companion R package, dmetar, is introduced at the beginning of the guide. It contains data sets and several helper functions for the meta and metafor package used in the guide. The programming and statistical background covered in the book are kept at a non-expert level, making the book widely accessible. Features • Contains two introductory chapters on how to set up an R environment and do basic imports/manipulations of meta-analysis data, including exercises • Describes statistical concepts clearly and concisely before applying them in R • Includes step-by-step guidance through the coding required to perform meta-analyses, and a companion R package for the book

Regression Analysis for Categorical Moderators

Author : Herman Aguinis
Publisher : Guilford Press
ISBN 13 : 9781572309692
Total Pages : 230 pages
Book Rating : 4.3/5 (96 download)

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Book Synopsis Regression Analysis for Categorical Moderators by : Herman Aguinis

Download or read book Regression Analysis for Categorical Moderators written by Herman Aguinis and published by Guilford Press. This book was released on 2004-01-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does the stability of personality vary by gender or ethnicity? Does a particular therapy work better to treat clients with one type of personality disorder than those with another? Providing a solution to thorny problems such as these, Aguinis shows readers how to better assess whether the relationship between two variables is moderated by group membership through the use of a statistical technique, moderated multiple regression (MMR). Clearly written, the book requires only basic knowledge of inferential statistics. It helps students, researchers, and practitioners determine whether a particular intervention is likely to yield dissimilar outcomes for members of various groups. Associated computer programs and data sets are available at the author's website (http: //mypage.iu.edu/ haguinis/mmr).

Semiparametric Single-index Predictive Regression

Author : Weilun Zhou
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (128 download)

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Book Synopsis Semiparametric Single-index Predictive Regression by : Weilun Zhou

Download or read book Semiparametric Single-index Predictive Regression written by Weilun Zhou and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Regression and Other Stories

Author : Andrew Gelman
Publisher : Cambridge University Press
ISBN 13 : 110702398X
Total Pages : 551 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Regression and Other Stories by : Andrew Gelman

Download or read book Regression and Other Stories written by Andrew Gelman and published by Cambridge University Press. This book was released on 2020-07-23 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical approach to using regression and computation to solve real-world problems of estimation, prediction, and causal inference.

Festschrift in Honor of R. Dennis Cook

Author : Efstathia Bura
Publisher : Springer Nature
ISBN 13 : 3030690091
Total Pages : 200 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Festschrift in Honor of R. Dennis Cook by : Efstathia Bura

Download or read book Festschrift in Honor of R. Dennis Cook written by Efstathia Bura and published by Springer Nature. This book was released on 2021-04-27 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of professor and renowned statistician R. Dennis Cook, this festschrift explores his influential contributions to an array of statistical disciplines ranging from experimental design and population genetics, to statistical diagnostics and all areas of regression-related inference and analysis. Since the early 1990s, Prof. Cook has led the development of dimension reduction methodology in three distinct but related regression contexts: envelopes, sufficient dimension reduction (SDR), and regression graphics. In particular, he has made fundamental and pioneering contributions to SDR, inventing or co-inventing many popular dimension reduction methods, such as sliced average variance estimation, the minimum discrepancy approach, model-free variable selection, and sufficient dimension reduction subspaces. A prolific researcher and mentor, Prof. Cook is known for his ability to identify research problems in statistics that are both challenging and important, as well as his deep appreciation for the applied side of statistics. This collection of Prof. Cook's collaborators, colleagues, friends, and former students reflects the broad array of his contributions to the research and instructional arenas of statistics.

Flexible Partially Linear Single Index Regression Models for Multivariate Survival Data

Author : Na Lei
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Flexible Partially Linear Single Index Regression Models for Multivariate Survival Data by : Na Lei

Download or read book Flexible Partially Linear Single Index Regression Models for Multivariate Survival Data written by Na Lei and published by . This book was released on 2013 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival regression models usually assume that covariate effects have a linear form. In many circumstances, however, the assumption of linearity may be violated. The present work addresses this limitation by adding nonlinear covariate effects to survival models. Nonlinear covariates are handled using a single index structure, which allows high-dimensional nonlinear effects to be reduced to a scalar term. The nonlinear single index approach is applied to modeling of survival data with multivariate responses, in three popular models: the proportional hazards (PH) model, the proportional odds (PO) model, and the generalized transformation model. Another extension of the PH and PO model is the handling of the baseline function. Instead of modeling it in a parametric way, which is fairly restrictive, or leaving it unspecified, which makes it impossible to calculate the survival and hazard functions, a weakly parametric approach is used here. As a result, the full likelihood can be applied for inference. The new developments are realized by adding a number of weakly parametric elements to the standard parametric regression models. The marginal baseline hazard functions are modeled using piecewise constants. Marginal survival functions are combined in using copula models, such as the Clayton model, to incorporate association among the multivariate responses. The nonlinear covariate effect is brought into the model through a smooth function with the single-index structure as the input. The smooth function is modeled using a spline. The performance of the PH, PO, and transformation models with the proposed extensions is evaluated through extensive simulation studies. The PH and PO models are also applied to a real-world data set. The results suggest that the proposed methods can capture the nonlinear covariate effects well, and that there is benefit to modeling the association between the correlated responses. Individual-level survival or hazard function estimates also provide information of interest to researchers. The proposed transformation model in particular is very promising. Some discussion of how this model may be further developed is provided.