Measurement Error Models

Parts of MEM

The regression model can be described by a conditional distribution of y given (z, ξ) and given an unknown parameter vector θ. As usual this distribution is represented by a probability density function f(y | z, ξ; θ) with respect to some underlying measure on the Borel σ-field of R. We restrict our attention to distributions that belong to the exponential family, i.e., we assume f to be of the form

$$f(y\vert z,\xi ;\beta ,\phi ) =\exp \left (\frac{y\eta - c(\eta )} {\phi } + a(y,\phi )\right )$$

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