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Constructing Quantitative Models Using Monotone Relationships
April 1995 (vol. 7 no. 2)
pp. 294-304

Abstract—Constructing quantitative models typically requires characterizing a system in terms of algebraic relationships and then using these relationships to compute quantitative values from numerical data. For real-life systems, such as computer operating systems, an algebraic characterization is often difficult, if not intractable. This paper proposes a statistical approach to constructing quantitative models using monotone relationships. Referred to as nonparametric interpolative-estimation for monotone functions (NIMF), our approach uses monotone relationships to search historical data for bounds that provide a desired level of statistical confidence. NIMF makes no assumption about the algebraic form of the monotone relationship, not even continuity.

We present two examples of applying NIMF to computer measurements, and compare NIMF’s confidence intervals with those of least-squares regression, a traditional technique that requires specifying an algebraic relationship. Our results suggest that when an algebraic characterization is not known with precision, using NIMF with an accurate monotone relationship can produce more accurate confidence intervals than employing least-squares regression with a polynomial approximation to the unknown algebraic relationship.

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Index Terms:
Monotone function, confidence intervals, estimation, statistics, qualitative reasoning.
Joseph L. Hellerstein, "Constructing Quantitative Models Using Monotone Relationships," IEEE Transactions on Knowledge and Data Engineering, vol. 7, no. 2, pp. 294-304, April 1995, doi:10.1109/69.382298
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