Asymptotic expansions for distributions of latent roots in multivariate analysis

AbstractAsymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)−1, where S1 is Wm(n1, Σ, Ω) and S2 is Wm(n2, Σ), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix Ω large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n−1S, where S in Wm(n, Σ), for large n, and S1S2−1, where S1 is Wm(n1, Σ) and S2 is Wm(n2, Σ), for large n1 + n2

Derivative moments for characteristic polynomials from the CUE

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.Comment: 31 pages, 3 figure

Self-enhancement: food for thought

Self-enhancement denotes a class of psychological phenomena that involve taking a tendentiously positive view of oneself. We distinguish between four levels of self-enhancement—an observed effect, an ongoing process, a personality trait, and an underlying motive—and then use these distinctions to organize the wealth of relevant research. Furthermore, to render these distinctions intuitive, we draw an extended analogy between self-enhancement and the phenomenon of eating. Among the topics we address are (a) manifestations of self-enhancement, both obvious and subtle, and rival interpretations; (b) experimentally documented dynamics of affirming and threatening the ego; and (c) primacy of self-enhancement, considered alongside other intrapsychic phenomena, and across different cultures. Self-enhancement, like eating, is a fundamental part of human nature

Positive intelligence illusions: on the relation between intellectual self-enhancement and psychological adjustment

The relation between self-enhancement and psychological adjustment has been debated for over 2 decades. This controversy is partly due to the variety of approaches implicated in the assessment of mainly self-enhancement but also psychological adjustment. We adopted a face-valid approach by statistically removing actual intellectual ability variance from self-rated intellectual ability variance. Study 1 (N? =?2,048), a concurrent Internet investigation, provided initial insight into the relation between intellectual self-enhancement and psychological adjustment. Study 2 (N?=?238), a longitudinal round-robin investigation, allowed a closer examination of the dynamic processes underlying this relation. Self-enhancement was positively linked to multiple indicators of intrapersonal and interpersonal adjustment, and predicted rank-order increases in adjustment over time. The links between intellectual self-enhancement and intrapersonal adjustment were mediated by self-esteem. Finally, the interpersonal costs and benefits of self-enhancement systematically varied depending on methodolog