Descriptive statistics for interval-valued observations in the presence of rules
type: Item
instance of: scholarly article
title: Descriptive statistics for interval-valued observations in the presence of rules
zbMATH Open document ID: 1114.62003
author: L. Billard
author: Edwin Diday
published in: Computational Statistics
publication date: 2007-05-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62-07
Mathematics Subject Classification ID: 62-08
zbMATH DE Number: 5158596
zbMATH Keywords: symbolic data
zbMATH Keywords: joint histogram
zbMATH Keywords: sample mean
zbMATH Keywords: logical dependency rules
describes a project that uses: SAS
MaRDI profile type: Publication
full work available at URL: s00180-006-0259-6
OpenAlex ID: W1989715751
cites work: Q2756630
cites work: Symbolic Data Analysis
cites work: Analysis of symbolic data. Exploratory methods for extracting statistical information from complex data
DOI: 10.1007/S00180-006-0259-6
description: scientific article; zbMATH DE number 5158596