Download or read book Series Estimation for Single Index Models Under Constraints written by Chaohua Dong and published by . This book was released on 2018 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a semiparametric single-index model is investigated. The link function is allowed to be unbounded and has unbounded support that answers a pending issue in the literature. Meanwhile, the link function is treated as a point in an infinitely many dimensional function space which enables us to derive the estimates for the index parameter and the link function simultaneously. This approach is different from the profile method commonly used in the literature. The estimator is derived from an optimization with the constraint of an identification condition for the index parameter, which addresses an important problem in the literature of single-index models.In addition, making the best use of a property of Hermite orthogonal polynomials, an explicit estimator for the index parameter is obtained. Asymptotic properties for the two estimators of the index parameter are established. Their efficiency is discussed in some special cases as well. The finite sample properties of the two estimators are demonstrated through an extensive Monte Carlo study and an empirical example.
Download or read book Another Look at Single Index Models Based on Series Estimation written by Chaohua Dong and published by . This book was released on 2016 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a semiparametric single-index model is investigated. The link function is allowed to be unbounded and has unbounded support that answers a pending issue in the literature. Meanwhile, the link function is treated as a point in an infinitely many dimensional function space which enables us to derive the estimates for the index parameter and the link function simultaneously. This approach is different from the profile method commonly used in the literature. The estimator is derived from an optimization with the constraint of identification condition for index parameter, which is a natural way but ignored in the literature.
Download or read book Estimation of Single Index Models written by Hidehiko Ichimura and published by . This book was released on 1987 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation for Single index and Partially Linear Single index Nonstationary Time Series Models written by Chaohua Dong 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 Topics in Regularized Single Index Model written by and published by . This book was released on 2015 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on extending the regularized single index model from two practical aspects. Firstly, we develop a regularized single index model that allows researchers to incorporate prior shape information to the link function. To achieve this, we first propose a method to the open question of univariate shape constrained smoothing spline problem that is required for estimating the link function. Secondly, we develop a regularized single index model that safeguards researchers against heavy-tailed error and outlier in response. The key idea, which also poses the main challenge, is the use of least absolute deviation as the loss function. We propose an efficient algorithm for estimating this model. Although we present both models with L1 regularization, our approaches can be generalize to other types of regularization on regression coefficients.
Download or read book Identification and Estimation of Single Index Models with Measurement Error and Endogeneity written by Yingyao Hu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Single index Models written by Xia Cui and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and finan- cial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM ap- proach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the re- sulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement. -- Generalized single-index model ; index coefficients ; estimating equations ; asymptotic properties ; iteration
Download or read book Generalized Single index Models written by Xia Cui and published by . This book was released on 2009 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and finan- cial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM ap- proach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the re- sulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement. -- Generalized single-index model ; index coefficients ; estimating equations ; asymptotic properties ; iteration
Download or read book Generalized Single Index Models written by Xia Cui and published by . This book was released on 2017 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM approach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the resulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement.
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 Regularized Estimation for Nonlinear Index Models and Nonlinear Additive Models written by and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In data analysis with a large number of variables, it often needs to identify the important variables and build a predictive model with them. To select the informative variables, regularizing the regression coefficients can often be adopted. To capture the possible nonlinear structures hidden in the data, some flexible link functions can be used. This thesis focuses on developing new methodologies and the corresponding computation algorithms for single index logistic models, single index Cox models, and additive index linear models with flexible link functions when regularization exists, and this thesis also makes use of the regularization in nonparametric additive Cox models. In our proposed methods, the unknown link functions are estimated using natural cubic smoothing splines and an L1-norm penalty is applied to yield a desired sparsity in the estimated index parameters for variable selection. We use a novel constraint to make the models identifiable. This constraint is different from commonly used constraints in other available single index models, which may not be proper for regularized estimation. We propose a data-dependent approach to estimate the tuning parameters in the smoothing splines, which allows us to calibrate only one tuning parameter in practice. Simulation studies demonstrate that our proposed methods have performance comparable to that of the Lasso-based linear regression methods when the true models are linear and have a clear advantage when the true models are nonlinear. We apply our proposed single index regularized logistic (SirLogit) regression method to the American Cancer Society younger breast cancer survivor data and our proposed single index regularized Cox (SirCox) regression method to a TCGA ovarian cancer dataset. The findings of our analysis are intuitively appealing.
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 Semiparametric Least Squares SLS and Weighted SLS Estimation of Single index Models written by Hidehiko Ichimura and published by . This book was released on 1991 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Semi parametric Estimation in Single index Models written by Peter Hall and published by . This book was released on 1991 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct Semiparametric Estimation of Single Index Models with Discrete Covariates written by Joel L. Horowitz and published by . This book was released on 1994 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Efficient Semiparametric Estimation in a Class of Single index Models written by M. Bonneu and published by . This book was released on 1994 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
