George A. F. Seber
University of Auckland
StatisticsEconometricsPopulationMathematicsSampling (statistics)
74Publications
25H-index
10.3kCitations
What is this?
Publications 74
#1Mohammad M. Salehi (Qatar University)H-Index: 9
#2George A. F. Seber (University of Auckland)H-Index: 25
An adaptive sample involves modifying the sampling design on the basis of information obtained during the survey while remaining in the probability sampling framework. Complete allocation sampling is an efficient and easily implemented 2‐phase adaptive sampling design that targets field effort to rare species and is logistically feasible. The population is partitioned into strata that contain (secondary) units, and a simple random sample of secondary units is selected from each of the strata. If...
#1George A. F. Seber (University of Auckland)H-Index: 25
In this chapter we assume once again that $$\boldsymbol{\theta }\in W$$. However our hypothesis H now takes the form of freedom equations, namely $$\boldsymbol{\theta }=\boldsymbol{\theta } (\boldsymbol{\alpha })$$, where $$\boldsymbol{\alpha }= (\alpha _{1},\alpha _{2},\ldots,\alpha _{p-q})'$$. We require the following additional notation. Let $$\boldsymbol{\Theta }_{\boldsymbol{\alpha }}$$ be the p × p − q matrix with (i, j)th element $$\partial \theta _{i}/\partial \alpha _{j}$$, which we ass...
#1George A. F. Seber (University of Auckland)H-Index: 25
Nonlinear models arise when E[y] is a nonlinear function of unknown parameters. Hypotheses about these parameters may be linear or nonlinear. Such models tend to be used when they are suggested by theoretical considerations or used to build non-linear behavior into a model. Even when a linear approximation works well, a nonlinear model may still be used to retain a clear interpretation of the parameters. Once we have established a nonlinear relationship the next problem is how to incorporate the...
#1George A. F. Seber (University of Auckland)H-Index: 25
Sometimes after a linear model has been fitted it is realized that more explanatory (x) variables need to be added, as in the following examples.
#1George A. F. Seber (University of Auckland)H-Index: 25
Let $$\boldsymbol{\theta }$$ be an unknown vector parameter, let G be the hypothesis that $$\boldsymbol{\theta }\in \varOmega$$, a p-dimensional vector space in $$\mathbb{R}^{n}$$, and assume that $$\mathbf{y} \sim N_{n}[\boldsymbol{\theta },\sigma ^{2}\mathbf{I}_{n}]$$.
#1George A. F. Seber (University of Auckland)H-Index: 25
Apart from Chap. 8 on nonlinear models we have been considering linear models and hypotheses. We now wish to extend those ideas to non-linear hypotheses based on samples of n independent observations $$x_{1},x_{2},\ldots,x_{n}$$ (these may be vectors) from a general probability density function $$f(x,\boldsymbol{\theta })$$, where $$\boldsymbol{\theta }= (\theta _{1},\theta _{2},\ldots,\theta _{p})'$$ and $$\boldsymbol{\theta }$$ is known to belong to W a subset of $$\mathbb{R}^{p}$$. We wish to...
#1George A. F. Seber (University of Auckland)H-Index: 25
We discuss the Multi-hypergeometric and Multinomial distributions and their properties with the focus on exact and large sample inference for comparing two proportions or probabilities from the same or different populations. Relative risks and odds ratios are also considered. Maximum likelihood estimation, asymptotic normality theory, and simultaneous confidence intervals are given for the Multinomial distribution. The chapter closes with some applications to animal populations, including multip...
#1George A. F. Seber (University of Auckland)H-Index: 25
We establish the asymptotic equivalence of several test procedures for testing hypotheses about the Multinomial distribution, namely the Likehood-ratio, Wald, Score, and Pearson’s goodness-of-fit tests. Particular emphasis is given to contingency tables, especially $$2\times 2$$ tables where exact and approximate test methods are given, including methods for matched pairs.
#1George A. F. SeberH-Index: 25