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 Semi Parametric Estimation of Generalized Partially Linear Single Index Models written by Yingcun Xia and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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:
Download or read book Estimation in Semiparametric Models written by Johann Pfanzagl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.
Download or read book Semiparametric and Nonparametric Methods in Econometrics written by Joel L. Horowitz and published by Springer Science & Business Media. This book was released on 2010-07-10 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distributions of unobserved random variables. Often, it is assumed that functions of interest are linear or that unobserved random variables are normally distributed. Such assumptions simplify estimation and statistical inference but are rarely justified by economic theory or other a priori considerations. Inference based on convenient but incorrect assumptions about functional forms and distributions can be highly misleading. Nonparametric and semiparametric statistical methods provide a way to reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. These methods are applicable to a wide variety of estimation problems in empirical economics and other fields, and they are being used in applied research with increasing frequency. The literature on nonparametric and semiparametric estimation is large and highly technical. This book presents the main ideas underlying a variety of nonparametric and semiparametric methods. It is accessible to graduate students and applied researchers who are familiar with econometric and statistical theory at the level taught in graduate-level courses in leading universities. The book emphasizes ideas instead of technical details and provides as intuitive an exposition as possible. Empirical examples illustrate the methods that are presented. This book updates and greatly expands the author’s previous book on semiparametric methods in econometrics. Nearly half of the material is new.
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 Nonlinear Time Series written by Jiti Gao and published by CRC Press. This book was released on 2007-03-22 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully
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 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 On Semiparametric M Estimation in Single index Regression written by Michel Delecroix and published by . This book was released on 2004 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semiparametric Methods in Econometrics written by Joel L. Horowitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many econometric models contain unknown functions as well as finite- dimensional parameters. Examples of such unknown functions are the distribution function of an unobserved random variable or a transformation of an observed variable. Econometric methods for estimating population parameters in the presence of unknown functions are called "semiparametric." During the past 15 years, much research has been carried out on semiparametric econometric models that are relevant to empirical economics. This book synthesizes the results that have been achieved for five important classes of models. The book is aimed at graduate students in econometrics and statistics as well as professionals who are not experts in semiparametic methods. The usefulness of the methods will be illustrated with applications that use real data.
Download or read book Nonparametric and Semiparametric Methods in Econometrics and Statistics written by William A. Barnett and published by Cambridge University Press. This book was released on 1991-06-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a 1988 symposium on the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data.
Download or read book A Method of Moments Estimator for Semiparametric Index Models written by Bas Donkers and published by . This book was released on 2008 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions for the parameters of interest, which are used in the second step within a method-of-moments framework to estimate the parameters of interest. The estimator is shown to be root N consistent and asymptotically normal. We extend the procedure to multiple equation models. Our identification conditions and estimation framework provide natural tests for the number of indices in the model. In addition we discuss tests of separability, additivity, and linearity of the influence of the indices.
Download or read book Towards Distribution free Interpretation Inference and Network Estimation written by Yue Gao (Ph.D.) and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the era of AI, statistical or machine learning methods towards distribution-free assumptions are becoming increasingly important due to the growing amount of data that is being collected and analyzed. Traditional parametric methods may not always be appropriate or may lead to model mis-specification and inaccurate results when dealing with large or complex data sets. Besides, as specific distributional assumptions or parametric modeling are removed, the challenge of model interpretation and prediction inference arises and has been currently at the forefront of research efforts. One problem of our interests in this regard is non-parametric or semi-parametric network estimation for data that are not independent. Specifically, influence network estimation from a multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less robust to model mis-specification, non-linearities and heterogeneities. In Chapter 2, we develop a semi-parametric approach based on the monotone single-index multi-variate autoregressive model (SIMAM) which addresses these challenges. In particular, rather than using standard parametric approaches, we use the monotone single index model (SIM) for network estimation. We provide theoretical guarantees for dependent data, and an alternating projected gradient descent algorithm. Significantly we achieve rates of the form O(T^{-1/3} \sqrt{s\log(TM)}) (optimal in the independent design case) where s is {he number of edges in the influence network that indicates the sparsity level, M is the number of actors and T is the number of time points. In addition, we demonstrate the performance of SIMAM both on simulated data and two real data examples, and show it outperforms state-of-the-art parametric methods both in terms of prediction and network estimation. Another aspect important for distribution-free or model-free learning is the interpretation, i.e. to make the complicated non-parametric predictive models explainable. A number of model-agnostic methods for measuring variable importance (VI) have emerged in recent times, which assess the difference in predictive power between a full model trained on all variables and a reduced model that omits the variable(s) of interest. However, these methods typically encounter a bottleneck when estimating the reduced model for each variable or subset of variables, which is both costly and lacks theoretical guarantees. To address this problem, Chapter 3 proposes an efficient and adaptable approach for approximating the reduced model while ensuring important inferential guarantees. Specifically, we replace the need for fully retraining a wide neural network with a linearization that is initiated using the full model parameters. By including a ridge-like penalty to make the problem convex, we establish that our method can estimate the variable importance measure with an error rate of O({1}/{\sqrt{n}), where n represents the number of training samples, provided that the ridge penalty parameter is adequately large. Furthermore, we demonstrate that our estimator is asymptotically normal, enabling us to provide confidence bounds for the VI estimates. Finally, we demonstrate the method's speed and accuracy under different data-generating regimes and showcase its applicability in a real-world seasonal climate forecasting example. In addition to semi-parametric network estimation and fast estimation of variable importance for interpretation, an efficient method for prediction inference without specific distributional assumptions on the data is of our interest as well. In Chapter 4, we present a novel, computationally-efficient algorithm for predictive inference (PI) that requires no distributional assumptions in the data and can be computed faster than existing bootstrap-type methods for neural networks. Specifically, if there are $n$ training samples, bootstrap methods require training a model on each of the n subsamples of size n-1; for large models like neural networks, this process can be computationally prohibitive. In contrast, the proposed method trains one neural network on the full dataset with ([epsilon], [delta]) -differential privacy (DP) and then approximates each leave-one-out model efficiently using a linear approximation around the neural network estimate. With exchangeable data, we prove that our approach has a rigorous coverage guarantee that depends on the preset privacy parameters and the stability of the neural network, regardless of the data distribution. Simulations and experiments on real data demonstrate that our method satisfies the coverage guarantees with substantially reduced computation compared to bootstrap methods.
