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Partially Linear Models

Partially Linear Models
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642577008

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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.


Nonparametric and Semiparametric Models

Nonparametric and Semiparametric Models
Author: Wolfgang Karl Härdle
Publisher: Springer Science & Business Media
Total Pages: 317
Release: 2012-08-27
Genre: Mathematics
ISBN: 364217146X

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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.


Semiparametric Inference in Generalized Mixed Effects Models

Semiparametric Inference in Generalized Mixed Effects Models
Author: Maria Jose Lombardia
Publisher:
Total Pages:
Release: 2018
Genre:
ISBN:

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The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines like-lihood approaches for mixed effects models, with kernel methods. Following the methodology of Hauml;rdle et al (1998), we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behavior of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.


Generalized Linear Models

Generalized Linear Models
Author: Robert Gilchrist
Publisher: Springer
Total Pages: 0
Release: 1985-10-14
Genre: Mathematics
ISBN: 9780387962245

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This volume consists of the published proceedings of the GLIM 95 Conference, held at Lancaster University, UK, from 16-19 September 1995. This is the second of such proceedings, the first of which was published as No 14 of the Springer-Verlag Lecture Notes in Statistics (Gilchrist, ed,1992). Since the 1992 conference there has been a modest update of the GLIM system, called GLIM 3.77. This incorporates some minor but pleasant enhancements and these are outlined in these proceedings by payne and Webb. With the completion of GLIM 3.77, future developments of the GLIM system are again under active review. Aitkin surveys possible directions for GLIM. one sOlMlWhat different avenue for analysing generalized linear models is provided by the GENSTAT system; Lane and payne discuss the new interactive facilities p ided by version 5 of GENSTAT. On the theory Side, NeIder extends the concept and use of quasi-likelihood, giving useful forms of variance function and a method of introducing a random element into the linear predictor. Longford discusses one approach to the analysis of clustered observations (subjects within groups). Green and Yandell introduce 'semi-parametric modelling', allowing a compromise between parametriC and non-parametriC modelling. They modify the linear predictor by the addition of a ( smooth) curve, and estimate parameters by maximising a penalised log-likelihood. Hastie and Tibshirani introduce generalized additive models, introducing a linear predictor of the form 11 = (X + Efj(xj), with the fj estimated from the data by a weighted average of neighbouring observations.


Semiparametric Regression for the Applied Econometrician

Semiparametric Regression for the Applied Econometrician
Author: Adonis Yatchew
Publisher: Cambridge University Press
Total Pages: 238
Release: 2003-06-02
Genre: Business & Economics
ISBN: 9780521012263

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This book provides an accessible collection of techniques for analyzing nonparametric and semiparametric regression models. Worked examples include estimation of Engel curves and equivalence scales, scale economies, semiparametric Cobb-Douglas, translog and CES cost functions, household gasoline consumption, hedonic housing prices, option prices and state price density estimation. The book should be of interest to a broad range of economists including those working in industrial organization, labor, development, urban, energy and financial economics. A variety of testing procedures are covered including simple goodness of fit tests and residual regression tests. These procedures can be used to test hypotheses such as parametric and semiparametric specifications, significance, monotonicity and additive separability. Other topics include endogeneity of parametric and nonparametric effects, as well as heteroskedasticity and autocorrelation in the residuals. Bootstrap procedures are provided.


Contributions in infinite-dimensional statistics and related topics

Contributions in infinite-dimensional statistics and related topics
Author: Enea G. Bongiorno
Publisher: Società Editrice Esculapio
Total Pages: 300
Release: 2014-05-21
Genre: Mathematics
ISBN: 8874887639

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The interest towards Functional and Operatorial Statistics, and, more in general, towards infinite-dimensional statistics has dramatically increased in the statistical community and in many other applied scientific areas where people faces functional data. This volume collects the works selected and presented at the Third Edition of the International Workshop on Functional and Operatorial Statistics held in Stresa, Italy, from the 19th to the 21st of June 2014 (IWFOS’2014). The meeting represents an opportunity of bringing together leading researchers active on these topics both for what concerns theoretical aspects and a wide range of applications in various fields. To promote collaborations with other important strictly related areas of infinite-dimensional Statistics, such as High Dimensional Statistics and Model Selection Procedures, this book hosts works in the latter research subjects too.


High Dimensional Inference in Partially Linear Models

High Dimensional Inference in Partially Linear Models
Author: Ying Zhu
Publisher:
Total Pages: 31
Release: 2017
Genre:
ISBN:

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We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_{i}=X_{i} beta_{0} g_{0}(Z_{i}) varepsilon_{i}$, where the parameter vector of interest $ beta_{0}$ is high dimensional but sparse (exactly or approximately) and $g_{0}$ is an unknown nuisance function. Both versions are shown to have the same asymptotic normal distribution and do not require the minimal signal condition for statistical inference of any component in $ beta_{0}$. Our method also works when the vector of covariates $Z_{i}$ is high dimensional provided that the function classes $ mathbb{E}(X_{ij} vert Z_{i})$s and $ mathbb{E}(Y_{i} vert Z_{i})$ belong to exhibit certain sparsity features, e.g., a sparse additive decomposition structure. We further develop a simultaneous hypothesis testing procedure based on multiplier bootstrap. Our testing method automatically takes into account of the dependence structure within the debiased estimates, and allows the number of tested components to be exponentially high.


Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference
Author: Michael R. Kosorok
Publisher: Springer Science & Business Media
Total Pages: 482
Release: 2007-12-29
Genre: Mathematics
ISBN: 0387749780

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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.