Abstract
The problem of the detection of outliers is meaningful only within the context of a given statistical model. The form of a statistic to be used as an outlier criterion depends upon the degree of specification of the distribution of the random variable in the model. In the situations most often occurring, only the form of the distribution is assumed known; the parameters are left unspecified. The outlier criterion in this case may contain estimates of parameters, a common example being any of the so-called studentized statistics. This dissertation is concerned with developing procedures for determining the distributions of members of a broad class of studentized statistics. A method requiring solution of an integral equation is developed and considered extensively in the case of a single sample from a normal population. A criterion for outliers in the linear model is defined and its distribution studied.
Gentle, James Eddie (1974). Distributions of studentized statistics useful as outlier criteria. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -170381.