Descriptive statistics for interval-valued observations in the presence of rules
The observations consist of rectangles \(R^j\) to which the bivariate variables of interest \(Y^j=(Y_1^j,Y_2^j)\) belong. The authors consider algorithms for construction of univariate and multivariate (joint) histograms for \(\{Y^j\}_{j=1,\dots,n}\) by \(\{R^j\}_{j=1,\dots,n}\), in the case where some additional information (rules) on the possible range of \(Y^j\) is known. E.g., it can be a rule \(Y_1<Y_2\). The true value of \(Y^j\) is assumed to be uniformly distributed over the parts of \(R^j\) which satisfy the rules. An algorithm for histogram construction with formulas for sample means and variances are considered. The cases of \(p\)-dimensional and histogram-valued data are discussed. Implementations of the algorithms as SAS macros are presented.
scientific article; zbMATH DE number 5158596