文章基本信息

标题：Minimum Bias Designs For Generalized Linear Models
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作者：Khidir M. Abdelbasit ; Sultan Qaboos University ; Sultanate of Oman Neil A. Butler 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2006
卷号：68
期号：04
出版社：Indian Statistical Institute
摘要：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.
关键词：Minimum bias design, generalized linear model, binary data, Poisson data, exponential data.