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We examined whether intra-family discrepancies in perceptions of the adolescent's competence and independence were associated with autonomy and also well-being for adolescents and parents. The latent discrepancy model was used to examine the ways that mothers and fathers consistently differed from their adolescent across measures of independence and competence regarding type 1 diabetes, a stressful context for families. One-hundred and eighty-five mothers, fathers, and adolescents (M age= 12.5 SD= 1.3) completed measures of the adolescent's independence in completing diabetes tasks, problems with diabetes management, adherence to the medical regimen, measures of wellbeing, and metabolic control. The latent discrepancy model was conducted via structural equation modeling that generated latent discrepancies from the adolescent for mothers and fathers. Both mothers and fathers viewed the adolescent's competence more negatively than did the adolescent. These discrepancies related to more parental encouragement of independence and adolescent autonomy, but also poorer metabolic control, and poorer parental psychosocial well-being. ThePublisher's Disclaimer: The following manuscript is the final accepted manuscript. It has not been subjected to the final copyediting, fact-checking, and proofreading required for formal publication. It is not the definitive, publisher-authenticated version. The American Psychological Association and its Council of Editors disclaim any responsibility or liabilities for errors or omissions of this manuscript version, any version derived from this manuscript by NIH, or other third parties. The published version is available at www.apa.org/journals/dev. results are interpreted within a developmental perspective that views discrepancies as reflecting normative developmental processes of autonomy, but associated with disruptions in well-being in the short term. NIH Public AccessKeywords parent-child relationship; autonomy; adolescence; parent adjustment; type 1 diabetes Adolescence is a time when children and their parents work toward a new type of relationship as adolescents experience socio-emotional and cognitive developments (Steinberg & Silk, 2002). As a consequence, adolescents and their parents frequently view the family (Carlson, Cooper, & Spradling, 1991) and their relationship in discrepant ways (Tein, Roosa, & Michaels, 1994). A key parent-child discrepancy involves views of adolescents' competence and independence (Holmbeck & O'Donnell, 1991), with adolescents perceiving themselves as more competent and independent than do parents. In this paper, we examine discrepancies between the adolescent's and the parent's views of the adolescent's competence and independence with respect to diabetes management. We utilize a developmental and transactional perspective that views the parent-child relationship as a dynamic one where both parent and adolescent develop Kim, Conger, Lorenz, & Elder, 2001). We examine how discrepancies across multiple metrics of independence and competence ...

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fr\'{e}chet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension $1$ and hence measure $0$) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky).Comment: Published in at http://dx.doi.org/10.1214/12-AAP899 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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We use Jacobi field arguments and the contraction mapping theorem to locate Fréchet means of a class of probability measures on locally symmetric Riemannian manifolds with non-negative sectional curvatures. This leads, in particular, to a method for estimating Fréchet mean shapes, with respect to the distance function ρ determined by the induced Riemannian metric, of a class of probability measures on Kendall's shape spaces. We then combine this with the technique of ‘horizontally lifting’ to the pre-shape spheres to obtain an algorithm for finding Fréchet mean shapes, with respect to ρ, of a class of probability measures on Kendall's shape spaces in terms of the vertices of random shapes. This gives us, for example, an algorithm for finding Fréchet mean shapes of samples of configurations on the plane which is expressed directly in terms of the vertices.

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As demonstrated in our previous work on T4, the space of phylogenetic trees with four leaves, the global, as well as the local, topological structure of the space plays an important role in the non-classical limiting behaviour of the sample Fréchet means of a probability distribution on T4. Nevertheless, the techniques used in that paper were specific to T4 and cannot be adapted to analyse Fréchet means in the space Tm of phylogenetic trees with m( 5) leaves. To investigate the latter, this paper first studies the log map of Tm, a generalisation of the inverse of the exponential map on a Riemannian manifold. Then, in terms of a modified version of the log map, we characterise Fréchet means in Tm that lie in top-dimensional or co-dimension one strata. We derive the limiting distributions for the corresponding sample Fréchet means, generalising our previous results. In particular, the results show that, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie.

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fréchet means) of independent nonidentically distributed random variables taking values in Riemannian manifolds. In order to prove these theorems we describe and prove a simple kind of Lindeberg-Feller central approximation theorem for vector-valued random variables, which may be of independent interest and is therefore the subject of a self-contained section. This vector-valued result allows us to clarify the number of conditions required for the central limit theorem for empirical Fréchet means, while extending its scope.