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Nonparametric inferences for additive models.

Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits a certain parametric form. In an attempt to address these issues, we extend the generalized likelihood ratio (GLR) tests to additive models, using the backfitting estimator. We demonstrate that under the null models, the newly proposed GLR statistics follow asymptotically rescaled chi-squared ...

<1 when n is large enough, the matrix ([I.sub.n] - [S*.sub.D][W.sub.M.sup.[-D]])[.sup.T]([I.sub.n] - [S*.sub.D][W.sub.M.sup.[-D]]) is positive definite. Denote its minimum eigenvalue by [[lambda].sub.0] (>

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