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  • Publication
    Open Access
    Derailment in adolescence: Factor analytic structure and correlates
    (Wiley, 2024)
    Ratner, Kaylin
    ;
    ;
    Li, Qingyi
    ;
    Rice, Melody Estevez
    ;
    Burrow, Anthony L.

    Derailment is the sense of being “off-course” in life. But what could this mean for adolescents, who are often establishing identity and self-direction for the first time? We examined the structure and correlates of the Derailment Scale and its short form, the Derailment Scale-6 (DS-6), among middle-to-late adolescents (N = 452). Both scales exhibited unidimensionality, but the DS-6 demonstrated superior fit and correlated with cross-sectional distress markers (e.g., greater depression, lower life satisfaction, strained sense of purpose). Breaking from adult-based research, we failed to find evidence that derailment related to adolescent identity exploration and commitment. In extending assessment of derailment to adolescence, this study invites exploration of this experience during a time characterized by substantial transition and the emergence of stable self-views.

      6  181
  • Publication
    Embargo
    A global test for heteroscedastic one-way FMANOVA with applications
    (Elsevier, 2024) ;
    Zhang, Jin-Ting
    ;
    Cheng, Ming-Yen

    Multivariate functional data are prevalent in various fields such as biology, climatology, and finance. Motivated by the World Health Data applications, in this study, we propose and examine a global test for assessing the equality of multiple mean functions in multivariate functional data. This test addresses the one-way Functional Multivariate Analysis of Variance (FMANOVA) problem, which is a fundamental issue in the analysis of multivariate functional data. While numerous analysis of variance tests have been proposed and studied for univariate functional data, only a limited number of methods have been developed for the one-way FMANOVA problem. Furthermore, our global test has the ability to handle heteroscedasticity in the unknown covariance function matrices that underlie the multivariate functional data, which is not possible with existing methods. We establish the asymptotic null distribution of the test statistic as a chi-squared-type mixture, which depends on the eigenvalues of the covariance function matrices. To approximate the null distribution, we introduce a Welch–Satterthwaite type chi-squared-approximation with consistent parameter estimation. The proposed test exhibits root-𝓃 consistency, meaning it possesses nontrivial power against a local alternative. Additionally, it offers superior computational efficiency compared to several permutation-based tests. Through simulation studies and applications to the World Health Data, we highlight the advantages of our global test.

      7  38
  • Publication
    Embargo
    Two-sample Behrens–Fisher problems for high-dimensional data: A normal reference F-type test
    (Springer, 2023) ;
    Wang, Pengfei
    ;
    Zhang, Jin-Ting

    The problem of testing the equality of mean vectors for high-dimensional data has been intensively investigated in the literature. However, most of the existing tests impose strong assumptions on the underlying group covariance matrices which may not be satisfied or hardly be checked in practice. In this article, an F-type test for two-sample Behrens–Fisher problems for high-dimensional data is proposed and studied. When the two samples are normally distributed and when the null hypothesis is valid, the proposed F-type test statistic is shown to be an F-type mixture, a ratio of two independent 𝒳2-type mixtures. Under some regularity conditions and the null hypothesis, it is shown that the proposed F-type test statistic and the above F-type mixture have the same normal and non-normal limits. It is then justified to approximate the null distribution of the proposed F-type test statistic by that of the F-type mixture, resulting in the so-called normal reference F-type test. Since the F-type mixture is a ratio of two independent 𝒳2-type mixtures, we employ the Welch–Satterthwaite 𝒳2-approximation to the distributions of the numerator and the denominator of the F-type mixture respectively, resulting in an approximation F-distribution whose degrees of freedom can be consistently estimated from the data. The asymptotic power of the proposed F-type test is established. Two simulation studies are conducted and they show that in terms of size control, the proposed F-type test outperforms two existing competitors. The good performance of the proposed F-type test is also illustrated by a COVID-19 data example.

      13  37
  • Publication
    Embargo
    A fast and accurate kernel-based independence test with applications to high-dimensional and functional data.
    (Elsevier, 2024)
    Zhang, Jin-Ting
    ;

    Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent, a so-called HSIC (Hilbert–Schmidt Independence Criterion)-based test has been proposed. Its null distribution is approximated either by permutation or a Gamma approximation. In this paper, a new HSIC-based test is proposed. Its asymptotic null and alternative distributions are established. It is shown that the proposed test is root-𝓃 consistent. A three-cumulant matched chi-squared-approximation is adopted to approximate the null distribution of the test statistic. By choosing a proper reproducing kernel, the proposed test can be applied to many different types of data including multivariate, high-dimensional, and functional data. Three simulation studies and two real data applications show that in terms of level accuracy, power, and computational cost, the proposed test outperforms several existing tests for multivariate, high-dimensional, and functional data.

      7  24