Functional Relations, Random Coefficients, and Nonlinear Regression with Application to Kinetic Data

  • Søren Johansen

Part of the Lecture Notes in Statistics book series (LNS, volume 22)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Søren Johansen
    Pages 1-8
  3. Søren Johansen
    Pages 9-35
  4. Søren Johansen
    Pages 36-51
  5. Søren Johansen
    Pages 52-70
  6. Søren Johansen
    Pages 71-97
  7. Back Matter
    Pages 115-126

About this book

Introduction

These notes on regression give an introduction to some of the techniques that I have found useful when working with various data sets in collaboration with Dr. S. Keiding (Copenhagen) and Dr. J.W.L. Robinson (Lausanne). The notes are based on some lectures given at the Institute of Mathematical Statistics, University of Copenhigen, 1978-81, for graduate students, and assumes a familiarity with statistical theory corresponding to the book by C.R. Rao: "Linear Statistical Inference and its Applications". Wiley, New York (1973) . The mathematical tools needed for the algebraic treatment of the models are some knowledge of finite dimensional vector spaces with an inner product and the notion of orthogonal projection. For the analytic treatment I need characteristic functions and weak convergence as the main tools. The most important statistical concepts are the general linear model for Gaussian variables and the general methods of maximum likelihood estimation as well as the likelihood ratio test. All these topics are presented in the above mentioned book by Rao and the reader is referred to that for details. For convenience a short appendix is added where the fundamental concepts from linear algebra are discussed.

Keywords

Coefficients Covariance matrix Estimator Lineares Modell Regression (Math.) Variance linear regression

Authors and affiliations

  • Søren Johansen
    • 1
  1. 1.Institute of Mathematical StatisticsUniversity of CopenhagenCopenhagen ØDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5244-3
  • Copyright Information Springer-Verlag New York 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90968-4
  • Online ISBN 978-1-4612-5244-3
  • Series Print ISSN 0930-0325
  • About this book