Download or read book Semiparamertic Dimension Reduction Model and Applications written by Ge Zhao and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the robust nonparametric kernel regression context, we prescribe a data driven method to select the trimming parameter and the bandwidth robustly. The estimator is obtained through solving estimating equations, and it controls the effect from outlying observations through a combination of weighting and trimming. We show asymptotic consistency, establish the estimation bias, variance properties and derive the asymptotic distribution of the resulting estimator. The finite sample performance of the estimator is illustrated through both simulation studies and analysis on a problem related to wind power generation, which motivated this study at the first place.We propose a general index model for survival data, which generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametrics and martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring as assumed in many dimension reduction methods for censored survival data. We establish the root-$n$ consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class forthe general index model. Numerical experiments are carried out to demonstrate the empirical performance of the proposed estimators and an application to an AIDS data further illustrates the usefulness of the work.Kidney transplantation is the most effective renal replacement therapy for renal failure patients. With the severe shortage of kidney supplies and for the clinical effectiveness of transplantation, it would be crucial to design objective measures, such as the Estimated Post-Transplant Survival (EPTS) score, to quantify the benefit that a renal failure patient would gain from a potential transplantation by comparing the expected residual lives of the same patient with and without transplant. However, in the current EPTS system, the mostdominant predictors are severe comorbidity conditions (such as diabetes) and age, which might preclude old and sick patients for receiving transplants. To help design a morefair score system, we propose a flexible and general covariate-dependent mean residual life model to estimate EPTS. Our method is both efficient and robust as the covariate effect is estimated via a semiparametrically efficient estimator, while the mean residual life function is estimated nonparametrically. We further provide a formula to predict the residual life increment potential for any given patients. Our method would facilitate allocating kidneys to patients who would have the largest residual life increment among all the eligibles. Our analysis of the kidney transplant data from the U.S. Scientific Registry of Transplant Recipients indicated that the most important predictor is the waiting time for transplantation: a shorter waiting time may lead to larger potential gains. We also identified an index which could serve as an additional important predictor if the waiting time is approximately between 1.5 years and three years. As our framework is general, we envision that our analytical strategies can be adopted to other organ transplantation settings.

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 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 Bayesian Non and Semi parametric Methods and Applications written by Peter Rossi and published by Princeton University Press. This book was released on 2014-04-27 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews and develops Bayesian non-parametric and semi-parametric methods for applications in microeconometrics and quantitative marketing. Most econometric models used in microeconomics and marketing applications involve arbitrary distributional assumptions. As more data becomes available, a natural desire to provide methods that relax these assumptions arises. Peter Rossi advocates a Bayesian approach in which specific distributional assumptions are replaced with more flexible distributions based on mixtures of normals. The Bayesian approach can use either a large but fixed number of normal components in the mixture or an infinite number bounded only by the sample size. By using flexible distributional approximations instead of fixed parametric models, the Bayesian approach can reap the advantages of an efficient method that models all of the structure in the data while retaining desirable smoothing properties. Non-Bayesian non-parametric methods often require additional ad hoc rules to avoid "overfitting," in which resulting density approximates are nonsmooth. With proper priors, the Bayesian approach largely avoids overfitting, while retaining flexibility. This book provides methods for assessing informative priors that require only simple data normalizations. The book also applies the mixture of the normals approximation method to a number of important models in microeconometrics and marketing, including the non-parametric and semi-parametric regression models, instrumental variables problems, and models of heterogeneity. In addition, the author has written a free online software package in R, "bayesm," which implements all of the non-parametric models discussed in the book.

Download or read book Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation written by Enzo Giacomini and published by . This book was released on 2017 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most prominent dimension reduction technique - functional principal components analysis - however, does not model time dependences embedded in functional data. In this paper we use dynamic semiparametric factor models (DSFM) to reduce dimensionality and analyse the dynamic structure of unknown random functions by means of inference based on their lower dimensional representation. We apply DSFM to estimate the dynamic structure of risk neutral densities implied by prices of option on the DAX stock index.

Download or read book Semiparametric Approaches for Dimension Reduction Through Gradient Descent on Manifold written by Qing Xiao and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional data arises at an unprecedented speed across various fields. Statistical models might fail on high-dimensional data due to the "curse of dimensionality". Sufficient dimension reduction (SDR) is to extract the core information through low-dimensional mapping so that efficient statistical models can be built while preserving the regression information in the high-dimensional data. We develop several SDR methods through manifold parameterization. First, we propose a SDR method, gemDR, based on local kernel regression without loss of information of the conditional mean E[Y|X]. The method, gemDR, focuses on identifying the central mean subspace (CMS). Then gemDR is extended to CS-gemDR for central subspace (CS), through the empirical cumulative distribution function. CS-OPG, a modified outer product gradient (OPG) method for CS, is developed as an initial estimator for CS-gemDR. The basis B of the CMS or CS is estimated by a gradient descent algorithm. An update scheme on a Grassmann manifold is to preserve the orthogonality constraint on the parameters. To determine the dimension of the CMS and CS, two consistent cross-validation criteria are developed. Our methods show better performance for highly correlated features. We also develop ER-OPG and ER-MAVE to identify the basis of CS on a manifold. The entire conditional distribution of a response given predictors is estimated in a heterogeneous regression setting through composite expectile regression. The computation algorithm is developed through an orthogonal updating scheme on a manifold. The proposed methods are adaptive to the structure of the random errors and do not require restrictive probabilistic assumptions as inverse methods. Our methods are first-order methods which are computationally efficient compared with second-order methods. Their efficacy is demonstrated through numerical simulation and real data applications. The kernel bandwidth and basis are estimated simultaneously. The proposed methods show better performance in estimation of the basis and its dimension.

Download or read book Semiparametric Ultra High Dimensional Model Averaging of Nonlinear Dynamic Time Series written by Jia Chen and published by . This book was released on 2016 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose semiparametric model averaging schemes for nonlinear dynamic time series regression models with a very large (ultra) number of covariates including exogenous regressors and auto-regressive lags. Our purpose is to obtain accurate forecasts of a response variable making use of a large number of conditioning variables in a nonparametric way. We propose two semiparametric schemes of dimension reduction among the exogenous regressors and the auto-regressors. (lags of the response variable). In the first scheme, we introduce a Kernel Sure Independence Screening (KSIS) technique to screen out the regressors whose marginal regression (or auto-regression) functions do not make significant contribution to estimating the joint multivariate regression function; and thus reduces the dimension of the regressors from a possible exponential rate to a certain polynomial rate, typically smaller than the sample size; we then propose a semiparametric penalised method of Model Averaging MArginal Regression (MAMAR) for the regressors and auto-regressors that survive the screening procedure, to further select the regressors that have significant effects on estimating the multivariate regression function and predicting the future values of the response variable. In the second scheme, we impose an approximate factor modelling structure on the ultra-high dimensional exogenous regressors and use a popular principal component analysis to estimate the latent common factors. We then apply the penalised MAMAR method to select the estimated common factors and the lags of the response variable that are significant. In each of the two schemes, we ultimately determine the optimal combination of the significant marginal regression and auto-regression functions. Under some regularity conditions, we derive some asymptotic properties for these two semiparametric dimension-reduction schemes. Numerical studies including both simulation and an empirical application are provided to illustrate the proposed methodology.

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 On Applications of Semiparametric Methods written by Zhijian Li and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In statistics, a model that includes both parametric and nonparametric components is called a semiparametric model. Often times in these models, we are only interested in the finite-dimensional parameters while taking the infinite-dimensional nonparametric component as a nuisance parameter. The theory of semiparametric methods provides an insight into the analysis of such models and gives rise to efficient estimators of the finite-dimensional parameters in these models. In this dissertation, I applied the semiparametric approach to four types of regression models with homogeneous errors, including the nonparametric models, partially linear models, single index models and the partially linear single index models.

Download or read book Semiparametric Regression with R written by Jaroslaw Harezlak and published by Springer. This book was released on 2018-12-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow applied book on semiparametric regression methods using R is intended to close the gap between the available methodology and its use in practice. Semiparametric regression has a large literature but much of it is geared towards data analysts who have advanced knowledge of statistical methods. While R now has a great deal of semiparametric regression functionality, many of these developments have not trickled down to rank-and-file statistical analysts. The authors assemble a broad range of semiparametric regression R analyses and put them in a form that is useful for applied researchers. There are chapters devoted to penalized spines, generalized additive models, grouped data, bivariate extensions of penalized spines, and spatial semi-parametric regression models. Where feasible, the R code is provided in the text, however the book is also accompanied by an external website complete with datasets and R code. Because of its flexibility, semiparametric regression has proven to be of great value with many applications in fields as diverse as astronomy, biology, medicine, economics, and finance. This book is intended for applied statistical analysts who have some familiarity with R.

Download or read book The Work of Raymond J Carroll written by Marie Davidian and published by Springer. This book was released on 2014-06-06 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Raymond J. Carroll's research and commentary on its impact by leading statisticians. Each of the seven main parts focuses on a key research area: Measurement Error, Transformation and Weighting, Epidemiology, Nonparametric and Semiparametric Regression for Independent Data, Nonparametric and Semiparametric Regression for Dependent Data, Robustness, and other work. The seven subject areas reviewed in this book were chosen by Ray himself, as were the articles representing each area. The commentaries not only review Ray’s work, but are also filled with history and anecdotes. Raymond J. Carroll’s impact on statistics and numerous other fields of science is far-reaching. His vast catalog of work spans from fundamental contributions to statistical theory to innovative methodological development and new insights in disciplinary science. From the outset of his career, rather than taking the “safe” route of pursuing incremental advances, Ray has focused on tackling the most important challenges. In doing so, it is fair to say that he has defined a host of statistics areas, including weighting and transformation in regression, measurement error modeling, quantitative methods for nutritional epidemiology and non- and semiparametric regression.

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 Modern Dimension Reduction written by Philip D. Waggoner and published by Cambridge University Press. This book was released on 2021-08-05 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github.

Download or read book Multivariate Time Series Analysis and Applications written by William W. S. Wei and published by John Wiley & Sons. This book was released on 2019-03-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis—Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.

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.

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.

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.