Truncated estimation in functional generalized linear regression models

Bi-level structured functional analysis for genome-wide association studies

Genome-wide association studies (GWAS) have led to great successes in identifying genotype-phenotype associations for complex human diseases. In such studies, the high dimensionality of single nucleotide polymorphisms (SNPs) often makes analysis difficult. Functional analysis, which interprets SNPs densely distributed in a chromosomal region as a continuous process rather than discrete observations, has emerged as a promising avenue for overcoming the high dimensionality challenges. However, the majority of the existing functional studies continue to be individual SNP based and are unable to sufficiently account for the intricate underpinning structures of SNP data. SNPs are often found in groups (e.g., genes or pathways) and have a natural group structure. Additionally, these SNP groups can be highly correlated with coordinated biological functions and interact in a network. Motivated by these unique characteristics of SNP data, we develop a novel bi-level structured functional analysis method and investigate disease-associated genetic variants at the SNP level and SNP group level simultaneously. The penalization technique is adopted for bi-level selection and also to accommodate the group-level network structure. Both the estimation and selection consistency properties are rigorously established. The superiority of the proposed method over alternatives is shown through extensive simulation studies. A type 2 diabetes SNP data application yields some biologically intriguing results.

C2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values

In this paper, a cubic Hermite spline interpolating scheme reproducing both linear polynomials and hyperbolic functions is considered. The interpolating scheme is mainly defined by means of integral values over the subintervals of a partition of the function to be approximated, rather than the function and its first derivative values. The scheme provided is C2 everywhere and yields optimal order. We provide some numerical tests to illustrate the good performance of the novel approximation scheme.