Parameter Cascading Method for Functional Data Analysis : Adaptive Penalized Smoothing, Estimating Semiparametric Additive Models and Inferring Differential Equation Models

Jiguo Cao

ISBN 10: 3330072385 / ISBN 13: 9783330072381

Published by LAP LAMBERT Academic Publishing, 2017

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - Many statistical models involve three distinct groups of variables: local or nuisance parameters, global or structural parameters, and complexity parameters. In this book, we introduce the parameter cascading method to estimate these statistical models, which treats one group of parameters as an explicit or implicit function of other parameters. The dimensionality of the parameter space is reduced, and the optimization surface becomes smoother. The Newton-Raphson algorithm is applied to estimate these three distinct groups of parameters in three levels of optimization, with the gradients and Hessian matrices written out analytically by the Implicit Function Theorem if necessary and allowing for different criteria for each level of optimization. Moreover, variances of global parameters are estimated by the Delta method and include the variation coming from complexity parameters. We also propose three applications of the parameter cascading method in functional data analysis, include adaptive penalized smoothing, estimating the generalized semiparametric additive models and inferring parameters in differential equations.

Seller Inventory # 9783330072381

Bibliographic Details

• Title: Parameter Cascading Method for Functional Data Analysis : Adaptive Penalized Smoothing, Estimating Semiparametric Additive Models and Inferring Differential Equation Models
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2017
• Language: English
• ISBN 10: 3330072385
• ISBN 13: 9783330072381
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 15D millimeters 220 millimeters width by 150 millimeters height by 15 millimeters depth
• Weight: 375 grams

About this title

Synopsis

Many statistical models involve three distinct groups of variables: local or nuisance parameters, global or structural parameters, and complexity parameters. In this book, we introduce the parameter cascading method to estimate these statistical models, which treats one group of parameters as an explicit or implicit function of other parameters. The dimensionality of the parameter space is reduced, and the optimization surface becomes smoother. The Newton-Raphson algorithm is applied to estimate these three distinct groups of parameters in three levels of optimization, with the gradients and Hessian matrices written out analytically by the Implicit Function Theorem if necessary and allowing for different criteria for each level of optimization. Moreover, variances of global parameters are estimated by the Delta method and include the variation coming from complexity parameters. We also propose three applications of the parameter cascading method in functional data analysis, include adaptive penalized smoothing, estimating the generalized semiparametric additive models and inferring parameters in differential equations.

About the Author

Dr. Jiguo Cao is the Canada Research Chair in Data Science and associate professor at the Department of Statistics and Actuarial Science, Simon Fraser University. His research interests include developing novel statistical methodologies and applications in functional data analysis and estimating parameters in differential equations from real data.