klukowski methods 2011

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The book presents the estimators of three relations: equivalence, tolerance, and preference, in a finite set of data items, based on multiple pairwise comparisons, assumed to be disturbed by random errors. The estimators were developed by the author. They can refer to binary (qualitative), multivalent (quantitative), and combined comparisons. The estimates are obtained on the basis of solutions to the discrete programming problems.

The estimators have been developed under weak assumptions on the distributions of comparison errors; in particular, these distributions can have non-zero expected values. The estimators have good statistical properties, including, especially importantly, consistency. Therefore, they produce good results in cases when other methods generate incorrect estimates. The precision of the estimators has been established with the use of simulation methods. The estimates can be validated in a versatile way. The whole estimation process, i.e. comparisons, estimation and validation can be computerized. The approach allows also for inference about the relation type – equivalence or tolerance, on the basis of binary data. Thus, it has features of data mining methods.

The estimators have been applied for ranking and grouping of data from some empirical sets. In particular, estimation of the tolerance relation (overlapping classification) was applied for determination of homogenous shapes of functions expressing profitability of treasury securities and was used for forecasting purposes.

The work has been supported by the grant No N N111434937 of the Polish Ministry of Science and Higher Education.


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