Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the ...

Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the ...

Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the ...

We prove the results stated in the main paper. We start by providing a brief summary of the notations used in the paper. Set [p] = {1, . . . , p} and for a subset J ⊂ [p], let |J | be its cardinality. Bold upper (resp. lower) case letters denote matrices (resp. vectors), and the same letter not bold represents its coefficients, e.g. aj denotes the jth entry of a. For an n × p matrix A with colu...

The independence assumption, although reasonable when examining cross-sectional data using single-factor experimental designs, is seldom verified by investigators. A Monte Carlo type simulation experiment was designed to examine the relationship between true Types I and II error probabilities in six multiple comparison procedures. Various aspects, such as patterns of means, types of hypotheses,...

There are numerous General Linear Model (GLM) statistical designs that may require multiple hypothesis testing (MHT) procedures that control the Type I error inflation that occurs with multiple tests. This study investigated familywise error rates (FWER) and statistical power rates of several alpha-adjustment MHT procedures in factorial ANOVA, but results apply broadly to GLM procedures. Of fou...

A general theory on rates of convergence of the least-squares projection estimate in multiple regression is developed. The theory is applied to the functional ANOVA model, where the multivariate regression function Ž is modeled as a specified sum of a constant term, main effects functions of . Ž one variable and selected interaction terms functions of two or more . variables . The least-squares...

This research is to provide a solution of one-way ANOVA without using transformation when variances are heteroscedastic and group sizes are unequal. Parametric boothstrap test (Krishnamoorthy, Lu, & Mathew, 2007) has been shown to be competitive with many other methods when testing the equality of group means. We extend the parametric bootstrap algorithm to a multiple comparison procedure. Simu...

This paper aims at bridging a gap between functional ANOVA modeling and recent advances in machine learning and kernel-based models. Functional ANOVA on the one hand extends linear ANOVA techniques to nonlinear multivariate models as smoothing splines, aiming to provide interpretability to an estimate and handling the curse of dimensionality. Multiple kernel learning (MKL) on the other hand is ...