On multidimensional contingency tables with categories defined by the empirical quantiles of the marginal data
Identifieur interne : 00A307 ( Main/Merge ); précédent : 00A306; suivant : 00A308On multidimensional contingency tables with categories defined by the empirical quantiles of the marginal data
Auteurs : Craig B. Borkowf [États-Unis]Source :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 2000.
English descriptors
- Teeft :
- Asymptotic, Asymptotic distribution, Asymptotic theory, Asymptotic variances, Bivariate, Bivariate data, Borkowf, Borkowf journal, Cell proportions, Conditional proportions, Covariance, Covariance formula, Descriptive statistics, Diverse nonparametric statistics, Empirical medians, Empirical multivariate, Empirical quantile, Empirical quantiles, Emqp, Emqp distribution, Emqp methods, Emqp tables, Emqp theory, Epidemiological studies, Estimation procedures, Estimation process, Extensive simulation studies, Food records, Intake data, Intraclass, Intraclass correlation, Large number, Marginal constraints, Marginal data, Marginal distributions, Marginal ranks, Marginal variables, Medial, Medial correlation, Median, Mult, Mult distribution, Multivariate, Multivariate data, Multivariate medial correlation, Multivariate ranks, Nonparametric, Numerical results, Nutritional epidemiology, Original data, Point estimates, Population quantiles, Quantile, Quantile correlation, Quantiles, Rank correlation, Several statistics, Special case, Statistical planning, Triangular weights, Trivariate, Trivariate intraclass correlation, Trivariate vitamin, Variance, Variance models.
Abstract
Abstract: Epidemiologists sometimes collect multivariate continuous data on a number of subjects and then wish to analyze the relationships and the agreement between these measurements. They may choose to compute the empirical quantiles (e.g., medians or quintiles) of each of these measurements and use these quantities to define the marginal categories of a multidimensional contingency table. Such contingency tables have the empirical multivariate quantile-partitioned (EMQP) distribution, an extension of the bivariate case studied by Borkowf et al. (1997, Biometrics 53, 1054–1069). In this paper, we present the general asymptotic theory for the EMQP distribution and nonparametric large sample procedures to estimate the variances of such tables from observed multivariate data. We define several statistics of interest to epidemiologists that can be calculated from EMQP tables, including the intraclass correlation, and present numerical results for these statistics where the original data come from certain underlying trivariate distributions. We also discuss the relationship of the EMQP distribution to other distributions commonly used in categorical data analysis. In addition, we apply EMQP methods to analyze an example from nutritional epidemiology. Finally, we discuss how EMQP theory and methods can unify the distribution theory and estimation procedures for diverse nonparametric statistics calculated from multivariate ranks or quantile-categories.
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DOI: 10.1016/S0378-3758(00)00127-0
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Borkowf</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>National Cancer Institute (NCI), Division of Clinical Sciences (DCS), Cancer Prevention Studies Branch (CPSB), 6006 Executive Blvd., Suite 321, MSC 7058, Bethesda, MD 20892-7058</wicri:regionArea><placeName><region type="state">Maryland</region></placeName></affiliation><affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Statistical Planning and Inference</title><title level="j" type="abbrev">JSPI</title><idno type="ISSN">0378-3758</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000">2000</date><biblScope unit="volume">91</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="33">33</biblScope><biblScope unit="page" to="51">51</biblScope></imprint><idno type="ISSN">0378-3758</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0378-3758</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Asymptotic</term><term>Asymptotic distribution</term><term>Asymptotic theory</term><term>Asymptotic variances</term><term>Bivariate</term><term>Bivariate data</term><term>Borkowf</term><term>Borkowf journal</term><term>Cell proportions</term><term>Conditional proportions</term><term>Covariance</term><term>Covariance formula</term><term>Descriptive statistics</term><term>Diverse nonparametric statistics</term><term>Empirical medians</term><term>Empirical multivariate</term><term>Empirical quantile</term><term>Empirical quantiles</term><term>Emqp</term><term>Emqp distribution</term><term>Emqp methods</term><term>Emqp tables</term><term>Emqp theory</term><term>Epidemiological studies</term><term>Estimation procedures</term><term>Estimation process</term><term>Extensive simulation studies</term><term>Food records</term><term>Intake data</term><term>Intraclass</term><term>Intraclass correlation</term><term>Large number</term><term>Marginal constraints</term><term>Marginal data</term><term>Marginal distributions</term><term>Marginal ranks</term><term>Marginal variables</term><term>Medial</term><term>Medial correlation</term><term>Median</term><term>Mult</term><term>Mult distribution</term><term>Multivariate</term><term>Multivariate data</term><term>Multivariate medial correlation</term><term>Multivariate ranks</term><term>Nonparametric</term><term>Numerical results</term><term>Nutritional epidemiology</term><term>Original data</term><term>Point estimates</term><term>Population quantiles</term><term>Quantile</term><term>Quantile correlation</term><term>Quantiles</term><term>Rank correlation</term><term>Several statistics</term><term>Special case</term><term>Statistical planning</term><term>Triangular weights</term><term>Trivariate</term><term>Trivariate intraclass correlation</term><term>Trivariate vitamin</term><term>Variance</term><term>Variance models</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Epidemiologists sometimes collect multivariate continuous data on a number of subjects and then wish to analyze the relationships and the agreement between these measurements. They may choose to compute the empirical quantiles (e.g., medians or quintiles) of each of these measurements and use these quantities to define the marginal categories of a multidimensional contingency table. Such contingency tables have the empirical multivariate quantile-partitioned (EMQP) distribution, an extension of the bivariate case studied by Borkowf et al. (1997, Biometrics 53, 1054–1069). In this paper, we present the general asymptotic theory for the EMQP distribution and nonparametric large sample procedures to estimate the variances of such tables from observed multivariate data. We define several statistics of interest to epidemiologists that can be calculated from EMQP tables, including the intraclass correlation, and present numerical results for these statistics where the original data come from certain underlying trivariate distributions. We also discuss the relationship of the EMQP distribution to other distributions commonly used in categorical data analysis. In addition, we apply EMQP methods to analyze an example from nutritional epidemiology. Finally, we discuss how EMQP theory and methods can unify the distribution theory and estimation procedures for diverse nonparametric statistics calculated from multivariate ranks or quantile-categories.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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