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Extra resources for Innovations in Classification, Data Science, and Information Systems: Proceedings of the 27th Annual Conference of the Gesellschaft für Klassifikation e.V., Brandenburg University of Technology, Cottbus, March 12–14, 2003

Sample text

5 ( e i + |ei|) bi+i : - bi + 2te^+ ai+i := ( Z T z ) - ^ Z T b i + i Gi+i := Zai+i - bi+i IF Wa - e^+ill > Acstop T H E N GO T O S T E P 2 R E T U R N a^+i, h^i After the vector ax is determined, the discrimination function is evaluated for each non-sampled unit, which is then classified as belonging to the class U[ if ^(xi) > 0 or to the class U2 if ^(xi) < 0. Then the ratio N[/N is used as an estimate of population respondent fraction Wi which allows to compute the population mean value estimator according to expression (4).

Figure 4 shows a simulation for b o t h cases. Here, with t h e used scale parameter sjsf = 2, t h e objective function Hn{ci,b^ Zn) has a third local maximum also in t h e case of nonparallel lines b u t again with a smaller height. T h e aim is now t o estimate the local maxima of /i(a, 6), or more precisely, the set M : = {(a'^,6) G ASI X R; h{a,b) has local maximum at (a"^,6)}. As for classical vertical regression, if the derivative of p is redescending, then His[{a, b, ZN) has several local maxima so t h a t we define MN{ZN) := .

Consequently, the probability distribution of population characteristics was equivalent to the mixture of adequate within-stratum probabihty distributions. For the stratum Ui mean values of the variable under study and all the auxiliary variables were set to 0, whereas for the stratum U2 all these mean values were set to 2. All variables were uncorrelated within strata and their withinstratum standard deviations were set to one. Stratum sizes were assumed to be constant in successive populations and equal to A^i = 600 and A^2 = 400, resulting in a population respondent fraction being equal to 60%.

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