3. Parametric Modelling – Deterministic Trends

  1. Richard E. Chandler1 and
  2. E. Marian Scott2

Published Online: 18 MAR 2011

DOI: 10.1002/9781119991571.ch3

Statistical Methods for Trend Detection and Analysis in the Environmental Sciences

Statistical Methods for Trend Detection and Analysis in the Environmental Sciences

How to Cite

Chandler, R. E. and Scott, E. M. (eds) (2011) Parametric Modelling – Deterministic Trends, in Statistical Methods for Trend Detection and Analysis in the Environmental Sciences, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119991571.ch3

Editor Information

  1. 1

    Department of Statistical Science, UCL, Gower Street, London WC1E 6BT, UK

  2. 2

    School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK

Publication History

  1. Published Online: 18 MAR 2011
  2. Published Print: 18 MAR 2011

ISBN Information

Print ISBN: 9780470015438

Online ISBN: 9781119991571

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Keywords:

  • bootstrap methods;
  • generalised linear models (GLMs);
  • linear trend;
  • multiple regression techniques;
  • parametric modelling

Summary

This chapter discusses the estimation and testing for situations in which μt is assumed to have a particular mathematical representation: this is an example of a parametric model. It focuses mostly on the case when the observations are regularly spaced. This is purely for notational convenience, since the basic ideas can be applied with little or no modification to irregularly spaced series. The chapter considers an extended class of regression models in which this assumption is relaxed. Generalised linear models (GLMs) have become a cornerstone of much statistical practice. With the exception of the standard multiple regression model, the methods introduced in the chapter are justified on the basis of large-sample approximations. When these approximations are not sufficiently accurate, computer-intensive methods often provide a feasible alternative. One of the most popular modern techniques is the bootstrap.

Controlled Vocabulary Terms

bootstrap method; linear trend