It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...

Genome-wide association studies (GWAS) are widely applied to analyze the genetic effects on phenotypes. With the availability of high-throughput technologies for metabolite measurements, GWAS successfully identified loci that affect metabolite concentrations and underlying pathways. In most GWAS, the effect of each SNP on the phenotype is assumed to be additive. Other genetic models such as rec...

A plethora of genetic association analyses have identified several genetic risk loci. Technological and statistical advancements have now led to the identification of not only common genetic variants, but also low-frequency variants, structural variants, and environmental factors, as well as multi-omics variations that affect the phenotypic variance of complex traits in a population, thus refer...

We examine a generalized F-test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedur...

BACKGROUND After the recent successes of genome-wide association studies (GWAS), one key challenge is to identify genetic variants that might have a significant joint effect on complex diseases but have failed to be identified individually due to weak to moderate marginal effect. One popular and effective approach is gene set based analysis, which investigates the joint effect of multiple funct...

The association of genetic variants with outcomes is usually assessed under an additive model, for example by the trend test. However, misspecification of the genetic model will lead to a reduction in power. More robust tests for association might therefore be preferred. A useful approach is to consider the maximum of the three test statistics under additive, dominant and recessive models (MAX3...

Most of the genome-wide association studies (GWASs) for human complex diseases have ignored dominance, epistasis and ethnic interactions. We conducted comparative GWASs for total cholesterol using full model and additive models, which illustrate the impacts of the ignoring genetic variants on analysis results and demonstrate how genetic effects of multiple loci could differ across different eth...

The concept of breeding values, an individual's phenotypic deviation from the population mean as a result of the sum of the average effects of the genes they carry, is of great importance in livestock, aquaculture, and cash crop industries where emphasis is placed on an individual's potential to pass desirable phenotypes on to the next generation. As breeding or genetic values (as referred to h...

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwis...

Breastfeeding has been an important survival trait during human history, though it has long been recognized that individuals differ in their exact breastfeeding behavior. Here our aims were, first, to explore to what extent genetic and environmental influences contributed to the individual differences in breastfeeding behavior; second, to detect possible genetic variants related to breastfeedin...