A Characterization of the log density smoothing spline ANOVA model
نویسندگان
چکیده
In this paper we introduce a characterization of the log density smoothing spline ANOVA model. We show that in a log density ANOVA model of order r (consisting of the main effects and all the interactions of order up to r), the joint density function is uniquely determined by the collection of all r dimensional marginal densities. Furthermore, the order r model is the largest log density ANOVA model under which the joint density function is uniquely determined by the r dimensional marginals. Our results are valid for log density ANOVA model with other general structures. In general, in log density ANOVA models the joint density function is uniquely determined by the marginal densities corresponding to the terms present in the ANOVA model. For example, the ANOVA model consists of main effects, the two way interactions η 12 , η 23 , η 13 , η 14 , η 34 , and the three way interaction η 134 is the largest log density ANOVA model under which the joint density is uniquely determined by the 12, 23, 134 marginals.
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