We consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates. For the nonparametric part we assume two models. In the first, the regression function is unspecified and smooth; in the second, the regression function is additive with smooth components. Depending on the model, the regression curve is estimated ...

We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as "half-sibling regression," is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the pot...

We prove that the topology of the additive group of the Banach space c0 is not induced by weakly almost periodic functions or, which is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. This answers, on the negative, questions of Megrelishvili [14] and Glasner and Megrelishvili [7]. We show, in contrast, that additive groups of Schwartz locall...

An experiment with a multiple-cue judgment task tested the hypothesis that humans can only abstract explicit representations of cue-criterion relations when the cues are related to the criterion by an additive function. It is proposed that the sequential and capacity-constrained nature of controlled, explicit thought can only induce and execute linear additive cue integration; non-additive envi...

The generalized additive model is a well established and strong tool that allows to model smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, substantial bias is to be expected. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functi...

We study the problem of estimating an unknown function from ergodic samples corrupted by additive noise. It is shown that one can consistently recover an unknown measurable function in this setting if the one dimensional distribution of the samples is comparable to a known reference distribution, and the noise is independent of the samples and has known mixing rates. The estimates are applied t...

1. We say that g(n) is additive if g(mn)=g(m)+g(n) holds for every coprime pairs m, n of positive integers . If, moreover, g(p') =g(p)' for every prime power pa , then g(n) is called strongly additive . By p, pi , p2 , . . ., q, qr , q2 , . . . we denote prime numbers, c, Cl, c2i . . . are suitable positive constants . F(n) and x(n) denote the largest and the smallest prime factor of n . The sy...

This paper discusses the additive prime divisor function A(n) := ∑ pα||n αp which was introduced by Alladi and Erdős in 1977. It is shown that A(n) is uniformly distributed (mod q) for any fixed integer q > 1.

Let Fq be a finite field with q elements and p ∈ Fq [X, Y ]. In this paper we study properties of additive functions with respect to number systems which are defined in the ring Fq [X, Y ]/p(X, Y )Fq [X, Y ]. Our results comprise distribution results, exponential sum estimations as well as a version of Waring’s Problem restricted by such additive functions. Similar results have been shown for q...