Abstract #301247

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JSM 2003 Abstract #301247
Activity Number: 27
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #301247
Title: Linear Equations with Random Variables
Author(s): Toshiro Tango*+
Companies: National Institute of Public Health
Address: 3-6 Minami, 2 Chome, Wako Saitama-ken 351-0197, , , Japan
Keywords: nutrition ; maximum likelihood estimator ; iterative method
Abstract:

This article proposes a new system of linear equations where variables are not constants but observed values of random variables. To solve the new linear equations or estimate the means of random variables and unknown observed values of random variables, two kinds of estimators, maximum likelihood estimator and proportional allotment estimator, are proposed. These estimators are derived by simple iterative methods. The new linear equations includes the ordinary linear equations as a special case where variances of the random variables are zero. The proposed methods are illustrated with the estimation problem of age-sex specific nutrient intakes based on National Nutrition Survey Data.

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