Common Models of Errors in Variables

Blurred observations can be described in multiple ways. If the errors occur as a scaling or shifting variable, we find ourselves in the frequently employed multiplicative or additive model of errors in variables. In these, the determinationKaiser, H. of the distribution or density function of the unblurred variable, under the assumption of independent errors, corresponds to some kind of deconvolution problem. We briefly present both models and point out their parallels. Special focus lies on the additive model, which was first studied in the late 1980 s and is still subject of further research. After a discussion of the traditional approach by virtue of Fourier transforms, we outline its developments until today. A distinction between known and unknown errors is made.