Functional relations, random coefficients, and nonlinear regression with application to kinetic data
type: Item
instance of: scholarly article
title: Functional relations, random coefficients, and nonlinear regression with application to kinetic data
zbMATH Open document ID: 0543.62051
published in: Lecture Notes in Statistics
publication date: 1984-01-01T00:00:00Z
review text: These notes are based on some lectures given by the author at the Institute of Mathematical Statistics, University of Copenhagen. The list of contents is as follows: Chapter 1: An example from physiology; Chapter 2: The general linear model; Chapter 3: The linear functional relation; Chapter 4: Random coefficient models; Chapter 5: Nonlinear regression; Chapter 6: Some examples of non-linear regression problems. An appendix gives basic concepts and results from linear algebra. The first chapter gives an example from physiology which motivates the problems studied in the later chapters. The second chapter discusses linear model theory when the observations are independent with the same variance and when the observations are correlated with known or unknown covariance matrix. The general linear model with estimated weights is studied in this chapter. The approach to the study of linear models throughout this chapter is geometric in nature. Let \((X_ i,Y_ i)\), 1\(\leq i\leq n\), be independent random variables distributed as bivariate normal with mean \((\xi_ i,\alpha +\beta \xi_ i)\) for 1\(\leq i\leq n\) and covariance matrix \(\sigma^ 2I\). This is not a linear model. The author studies the problems of estimation of \((\alpha,\beta,\xi_ 1,...,\xi_ n,\sigma^ 2)\) in Chapter 2. Asymptotic properties of the estimators and test statistics based on them are derived. Random coefficient models are discussed in Chapter 3. Here linear models with Gaussian errors are considered. Tests for the specification of the model and tests of hypotheses within the model are derived. Asymptotic properties of the estimator in a nonlinear regression model \(Y\simeq N_ n(f(\theta),\sigma^ 2I)\), \(\theta \in \Theta \subset R^ p\), are derived in Chapter 4. A likelihood ratio test for testing the hypothesis of the form \(H_ o:\theta =\theta(\beta)\), \(\beta \in B\), \(\theta\) (B)\(\subset \Theta\) is derived and its limiting distribution is obtained. An approximation to the distribution o…
reviewed by: B. L. S. Prakasa Rao
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 3864316
zbMATH Keywords: model specification tests
zbMATH Keywords: linear functional relation
zbMATH Keywords: Random coefficient models
zbMATH Keywords: general linear model with estimated weights
zbMATH Keywords: Gaussian errors
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: residual sum of squares
zbMATH Keywords: normal radius curvature
zbMATH Keywords: examples
author: Søren Johansen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3864316