Minimum bias designs for generalized linear models

Khidir M. Abdelbasit, Neil A. Butler

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Minimum bias (all bias) designs for the linear model were proposed by Box and Draper. In this article we extend their results to generalized linear models. We show that, in the canonical case, the minimum bias design density is: (a) proportional to the weight function reflecting the importance of each design point, and (b) inversely proportional to the observation variance at each point. We also derive minimum bias design densities in non-canonical cases. Implications for binary, Poisson and exponential data are considered in the examples. From these examples we observe that when the experimenter is mainly interested in the mean of the Binomial, Poisson or exponential distribution, rather than the canonical parameter, and if the weight function is chosen to be inversely proportional to the variance of the maximum likelihood estimator of the mean, minimum bias designs are uniform. These uniform designs automatically minimize the bias/standard error ratio and the mean square error/variance ratio.

Original languageEnglish
Pages (from-to)587-599
Number of pages13
JournalSankhya: The Indian Journal of Statistics
Volume68
Issue number4
Publication statusPublished - 2006

Fingerprint

Generalized Linear Model
Directly proportional
Weight Function
Variance Ratio
Uniform Design
Binomial distribution
Poisson distribution
Standard error
Exponential distribution
Mean square error
Maximum Likelihood Estimator
Design
Generalized linear model
Linear Model
Siméon Denis Poisson
Binary
Minimise

Keywords

  • Binary data
  • Exponential data
  • Generalized linear model
  • Minimum bias design
  • Poisson data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Minimum bias designs for generalized linear models. / Abdelbasit, Khidir M.; Butler, Neil A.

In: Sankhya: The Indian Journal of Statistics, Vol. 68, No. 4, 2006, p. 587-599.

Research output: Contribution to journalArticle

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