For manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure: first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution; second, it emplo...

Abstract Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors the estimated curve. Centring often applied by default because they thought to yield lowest out any constraint, but this claim has not been investigated. We show that whether centring optimal depends on response d...

We discuss some aspects of approximating functions on high-dimensional data sets with additive functions or ANOVA decompositions, that is, sums of functions depending on fewer variables each. It is seen that under appropriate smoothness conditions, the errors of the ANOVA decompositions are of order O(n) for indendent predictor variables and approximations using sums of functions of up to m var...

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 ...