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Optimal cutpoints for random observations

by Schmidt, M; Schwabe, R..

Series: 2014-03, Preprints

62K05 Optimal designs

For the discretisation of a continuous random variable into different categories the choice of cutpoints is necessary. A popular application is the contingent valuation method. As the choice of cutpoints directly effects the quality of the parameter estimates optimal cutpoints are desirable in order to obtain the most accurate estimates. We consider an arbitrary number of cutpoints and determine optimal cutpoints for the exponential and Gumbel distribution and prove that the c-optimal cutpoints for the location parameter of the logistic distribution have corresponding equal category probabilities. Furthermore, we show that in the limiting case for infinitely many cutpoints there is no loss of information.

c -optimality, cutpoints, exponential distribution, Gumbel distribu- tion, logistic distribution, multinomial distribution