Skip to Main Content
Mathematical Statistics
book

Mathematical Statistics

by Dieter Rasch, Dieter Schott
March 2018
Beginner content levelBeginner
688 pages
17h 32m
English
Wiley
Content preview from Mathematical Statistics

4Linear Models – General Theory

4.1 Linear Models with Fixed Effects

The theory of linear statistical models plays an important role in the applications. Mainly the standard methods of analysis of variance and regression analysis have become firmly established in evaluating biological and technological experiments.

In this chapter we introduce the general theory concerning methods of analysis of variance and regression analysis with fixed effects. In the following Ω ⊂ Rn denotes a p‐dimensional linear subspace with p < n called parameter space, and θ ∈ Ω denotes a parameter vector with n coordinates θi(i = 1,  … , n).

Further, let Y be an n‐dimensional random variable (a random vector) with components yi(i = 1,  … , n) and realisations Y from the n‐dimensional sample space Rn. Finally, let e be an n‐dimensional random variable with E(e) = 0n, var(e) = σ2V, where V is a symmetric and positive definite matrix of size (n, n) and rank n. For constructing tests and confidence intervals, we will later suppose that e (and hence also Y) are n‐dimensional normally distributed (satisfy n‐variate normal distributions).

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Essentials of Mathematical Statistics

Essentials of Mathematical Statistics

Brian Albright
Exercises and Solutions in Statistical Theory

Exercises and Solutions in Statistical Theory

Lawrence L. Kupper, Brian. H Neelon, Sean M. O'Brien

Publisher Resources

ISBN: 9781119385288Purchase book