Penalized Spline Estimation for Partially Linear Single Index Models PDF Download
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Author: Yan Yu
Publisher:
ISBN:
Category :
Languages : en
Pages : 258
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Author: Yan Yu
Publisher:
ISBN:
Category :
Languages : en
Pages : 258
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Author: Yingcun Xia
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Chaohua Dong
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Lili Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 76
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Book Description
"The partially linear model (PLM) is a flexible extension of both the linear model and nonparametric model of time series. The vector partially linear model (VPLM) is an extension of PLM when there are a set of observations at one time point from several sources. Smoothing spline is one of the popular approaches for PLM estimation. This thesis extends the smoothing spline approach to a few VPLMs and presents algorithms to compute the estimates. Then, we apply the smoothing spline based vector partially linear model (SSBVPLM) approach to Global Positioning System (GPS) applications. In an unfavorable environment, the accuracy of position estimates, which are usually computed by the least squares (LS) method based on the linear model, can be impaired due to system errors. In order to account the system errors, we use the vector partially linear models instead of the linear models. We apply the SSBVPLM estimation techniques to kinematic and static relative positioning, based on both code and carrier phase measurements. The simulations show that the SSBVPLM approach can yield more accurate position estimates than the LS approach." --
Author: Chen Wang
Publisher:
ISBN:
Category : Additive functions
Languages : en
Pages :
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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.
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
ISBN: 3642577008
Category : Mathematics
Languages : en
Pages : 210
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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.
Author: Grace Wahba
Publisher: SIAM
ISBN: 9781611970128
Category : Mathematics
Languages : en
Pages : 181
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This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Author: Maria João Costa
Publisher:
ISBN:
Category :
Languages : en
Pages : 336
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Author: Kukatharmini Tharmaratnam
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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This paper is about S-estimation for penalized regression splines. Penalized regression splines are one of the currently most used methods for smoothing noisy data. The estimation method used for fitting such a penalized regression spline model is mostly based on least squares methods, which are known to be sensitive to outlying observations. In real world applications, outliers are quite commonly observed. There are several robust estimation methods taking outlying observations into account. We define and study S-estimators for penalized regression spline models. Hereby we replace the least squares estimation method for penalized regression splines by a suitable S-estimation method. By keeping the modeling by means of splines and by keeping the penalty term, though using S-estimators instead of least squares estimators, we arrive at an estimation method that is both robust and flexible enough to capture non-linear trends in the data. Simulated data and a real data example are used to illustrate the effectiveness of the procedure.
Author: Jingwei Wu
Publisher:
ISBN:
Category : Biometry
Languages : en
Pages : 150
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Book Description
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.
