Classical testing in functional linear models

We extend four tests common in classical regression – Wald, score, likelihood ratio and F tests – to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.     

Collective Action as the Material Expression of Opinion-Based Group Membership

In this article, we argue that progress in the study of collective action rests on an increasingly sophisticated application of the social identity approach. We develop the view, however, that the application of this theoretical perspective has been limited by theoretical and empirical difficulties in distinguishing between social categories and psychological groups. These problems have undermined the ability of researchers to correctly specify the collective identities that actually underpin many instances of collective action. As a partial solution to this problem we focus on collective identities based on shared opinion (opinion-based groups). We develop the proposition that much collective action reflects the crystallization or instantiation of opinion-based groups. We also outline an intervention aimed at stimulating commitment to collective action through group-based interaction involving opinion-based group members. We conclude by emphasizing that opinion-based groups tend to be most successful when they present themselves as being representative or aligned with dominant, positively valued social categories such as nations.     

Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis

This paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized splines; and (2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo‐likelihood ratio test is proposed, and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite‐sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ‐power of sleep electroencephalograms of subjects with sleep‐disordered breathing and matched controls.     

The social contract revisited: a re-examination of the influence individualistic and collectivistic value systems have on the psychological wellbeing of young people

ABSTRACT

The prevalence of psychological health problems experienced by young people living in Western societies is increasing. Evidence suggests the cultural dynamism of individualism may play a role in this, but this evidence is conflicting. Here, we focus on both the concepts of individualism and collectivism, distinguishing between their horizontal and vertical dimensions. We examine the influence of these dimensions on the psychological wellbeing of a sample of 507 Australian emerging adults (aged 18–25). We found that orientations towards vertical (but not horizontal) individualism predicted lower levels of psychological wellbeing, while orientations towards horizontal (but not vertical) collectivism predicted higher psychological wellbeing. These findings add clarity to the way in which key Western social values play an understated role in the increasing prevalence of psychological health problems experienced by young people today. They also provide an understanding of how various traits embedded within these concepts relate to psychological wellbeing.     

On probability matching priors

First‐order probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to a second order of approximation. The authors show that the matching priors developed by Peers (1965) and Tibshirani (1989) are readily and uniquely implemented in a third‐order approximation to the posterior marginal density. The authors further show how strong orthogonality of parameters simplifies the arguments. Several examples illustrate their results.     

Higher-order approximations for interval estimation in binomial settings

In this paper we revisit the classical problem of interval estimation for one-binomial parameter and for the log odds ratio of two binomial parameters. We examine the confidence intervals provided by two versions of the modified log likelihood root: the usual Barndorff-Nielsen's r^*$r^{*}$ and a Bayesian version of the r^*$r^{*}$ test statistic.