title: Linear equations with random variables.
abstract: A system of linear equations is presented where the unknowns are unobserved values of random variables. A maximum likelihood estimator assuming a multivariate normal distribution and a non-parametric proportional allotment estimator are proposed for the unobserved values of the random variables and for their means. Both estimators can be computed by simple iterative procedures and are shown to perform similarly. The methods are illustrated with data from a national nutrition survey in Japan.
authors.affiliation: Department of Technology Assessment and Biostatistics, National Institute of Public Health, 3-6 Minami 2 chome, Wako, Saitama 351-0197, Japan. tango@niph.go.jp
authors.forename: Toshiro
authors.initials: T
authors.lastname: Tango
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D002648:Child; D002675:Child, Preschool; D005260:Female; D006801:Humans; D007223:Infant; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D009749:Nutrition Surveys