Flexible Regression Models for Functional Responses PDF Download

Author: Janet S Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 117

View

Book Description

Author: Hyung Park
Publisher:
ISBN:
Category :
Languages : en
Pages :

View

Book Description
To deal with this problem, we impose a constraint on the model space, giving the orthogonality between the main and the interaction effects. This modeling method is particularly appealing in the functional regression context, since a functional predictor, due to its infinite dimensional nature, must go through some sort of dimension reduction, which essentially involves a main effect model misspecication. The main effect and the interaction effect can be estimated separately due to the orthogonality between the two effects, which side-steps the issue of misspecication of the main effect. The proposed approach extends the modied covariate approach of [Tian et al., 2014] into an additive regression model framework. We impose a concave penalty in estimation, and the method simultaneously selects functional/scalar treatment effect modifiers that exhibit possibly nonlinear interaction effects with the treatment indicator. The dissertation concludes in Chapter 6.

Author: Jian Qing Shi
Publisher: CRC Press
ISBN: 1439837732
Category : Mathematics
Languages : en
Pages : 218

View

Book Description
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author’s website.

Author: Osval Antonio Montesinos López
Publisher: Springer Nature
ISBN: 3030890104
Category : Technology & Engineering
Languages : en
Pages : 707

View

Book Description
This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.

Author: David Ruppert
Publisher: Cambridge University Press
ISBN: 9780521785167
Category : Mathematics
Languages : en
Pages : 408

View

Book Description
Even experts on semiparametric regression should find something new here.

Author: Hassan Doosti
Publisher: Springer Nature
ISBN: 3031665015
Category :
Languages : en
Pages : 309

View

Book Description

Author: James Ramsay
Publisher: Springer Science & Business Media
ISBN: 0387981853
Category : Computers
Languages : en
Pages : 213

View

Book Description
The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Author: Boyi Hu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

View

Book Description
The conventional method for functional quantile regression is to fit the regression model for each quantile of interest separately. The slope function of the regression, as a bivariate function indexed by time and quantile, is actually estimated as a univariate function of time only by first fixing the quantile. This estimation strategy has two major limitations. The monotonicity of conditional quantiles can not be guaranteed, and the smoothness of the slope estimator as a bivariate function can not be controlled. We develop a new framework for functional quantile regression to overcome the two limitations. We propose to simultaneously fit the functional quantile regression model for multiple quantiles under some constraints so that the estimated quantiles satisfy the monotonicity conditions. Meanwhile, the smoothness of the slope estimator is controlled. Motivated by an application of modeling the impact of daily temperature, annual precipitation and irrigation system on soybean yield, we propose two locally sparse estimation methods under a semi-parametric functional quantile regression model. In the target application, the daily temperature is a functional predictor, and the influence of daily temperature on soybean yield may not always exist during the whole growing season. We aim to identify the time regions where the influence exists. For this purpose, in two projects, we use two different penalized estimation methods, functional SCAD and modified group lasso, to obtain locally sparse estimations for the bivariate slope function associated with the functional predictor. Focusing on the soybean yield application introduced above, we further propose a novel semi-parametric functional generalized linear model (FGLM) to analyze the relationship between the environmental factors and the soybean yield. In this project, we consider the data from different years as from different populations due to the fact that the climate conditions can be very different year by year. Based on the new assumption, the main challenge is that we only have limited number of observations for each year. To solve this issue, we combine a density ratio model with the proposed semi-parametric FGLM so that the new framework can be fitted using the pool data. We propose to use a combination of penalized B-spline and empirical likelihood method to fit the model. The proposed method is highly flexible and robust to model misspecification.

Author: Mikis D. Stasinopoulos
Publisher: CRC Press
ISBN: 1351980378
Category : Mathematics
Languages : en
Pages : 641

View

Book Description
This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.

Author: Yanan Fan
Publisher: Academic Press
ISBN: 0128158638
Category : Business & Economics
Languages : en
Pages : 302

View

Book Description
Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian revolution in regression modeling, for use in advanced econometric and statistical analysis where datasets are characterized by complexity, multiplicity, and large sample sizes, necessitating the need for considerable flexibility in modeling techniques. It reviews three forms of flexibility: methods which provide flexibility in their error distribution; methods which model non-central parts of the distribution (such as quantile regression); and finally models that allow the mean function to be flexible (such as spline models). Each chapter discusses the key aspects of fitting a regression model. R programs accompany the methods. This book is particularly relevant to non-specialist practitioners with intermediate mathematical training seeking to apply Bayesian approaches in economics, biology, finance, engineering and medicine. Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners Focuses on approaches offering both superior power and methodological flexibility Supplemented with instructive and relevant R programs within the text Covers linear regression, nonlinear regression and quantile regression techniques Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis ‘in the wild’