Linear Estimation of a Regression Relationship from Censored Data—Part II Best Linear Unbiased Estimation and Theory

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Abstract
In many regression problems, data on the dependent variable are censored; that is, the values of some observations are known only to be above or else below some value. Such data often arise in accelerated life testing where life is the dependent variable and temperature or stress is the independent variable, and some test units have not failed at the time of the analysis. In such situations, the standard techniques of least squares estimation for the parameters of a linear regression model cannot be used, since the values of the censored observations are not known. This is Part II of a two-part series on the theory and application of linear estimation methods for regression analysis using the ordered observations of censored data. Part II deals with best (minimum variance) linear unbiased estimators for the parameters of a linear regression model. The use of these methods is illustrated with analyses of censored data from tandem specimens in a creep-rupture test on an alloy. The theory underlying the various methods given in this series is also presented.