DESIGN AND INFERENCE FOR DISCRIMINATING BETWEEN TWO COMPETING LINEAR REGRESSION MODELS

概要

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The problem of discriminating between two competing simple linear regression models <var>MI</var> and <var>MII</var> is discussed in this paper. Model <var>MI</var> is nested within model <var>MII</var> with a common linear term being present in both models with respect to an explanatory variable and an additional quadratic term with respect to the same explanatory variable being present in <var>MII</var>. The first criterion function for discrimination between <var>MI</var> and <var>MII</var> is in terms of minimizing the variance of the least squares estimated coefficient of the quadratic term. A lower bound is obtained for this variance. Two designs are presented satisfying this lower bound in two experimental regions. New criterion functions for discriminating between <var>MI</var> and <var>MII</var> are given based on maximizing the difference between the fitted values of <var>n</var> observations under <var>MI</var> and <var>MII</var>, and maximizing the difference between the predicted values under <var>MI</var> and <var>MII</var>. Several results are obtained for demonstrating the performances of these designs under two new criterion functions. We also present five general classes of designs and demonstrate their sharp relative performances with respect to our criterion functions. Some results for discriminating between two competing general linear models <var>MIII</var> and <var>MIV</var> are also given.
日本統計学会の論文
2009-06-01