Modified estimator of the contribution rates of population eigenvalues

Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The improvement of the modified estimators over the classical estimator are proved theoretically in view of their risks. We also checked numerically that the drawback of the classical estimator, namely the underestimation of the dimension in principal component analysis or factor analysis, are corrected in the modification.Comment: 25 page

Teacher guided reporting in a primary literacy context : the stepping stones of mode and interaction

In this paper I take Gibbons' notion of Teacher Guided Reporting (TGR) and explore whether the features she identifies as being crucial in a science lesson with 9-10 year olds also are found in a literacy lesson with 5-6 year olds. The findings support Gibbons' claims for linguistic sequencing of tasks, degree of student initiations and role of teacherstudent interaction. The analysis suggests a wider variety of mode continua which underpin the linguistic sequencing of literacy tasks; and that these combine with the developing focus of teacher feedback across the series of TGR interactions in three main strands - language, content and process - which together promote the learners' language development towards written academic registers appropriate for schooling in English

Gender Relations and Women’s Off-farm Employment: a critical analysis of discourses

End of Project ReportThis project addresses gender relations on dairy farms in Irish Republic. Its aim was to explore the way women who are married to farmers but who are employed in paid employment off the farm are constructed in agricultural policy discourse. It was proposed that discourses encapsulate the values and interests of powerful actors and are constitutive in their effect. Hence they are implicated in women’s experience of life within a ‘farm family’. Following on from this it may be said that women’ s continued subordination in Irish farming or indeed their chances of achieving equal status are circumscribed by dominant discourses

Asymptotic Distribution of Wishart Matrix for Block-wise Dispersion of Population Eigenvalues

This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately normalized eigenvectors and eigenvalues asymptotically generate two Wishart matrices and one normally distributed random matrix, which are mutually independent. For a family of orthogonally equivariant estimators, we calculate the asymptotic risks with respect to the entropy or the quadratic loss function and derive the asymptotically best estimator among the family. We numerically show 1) the convergence in both the distributions and the risks are quick enough for a practical use, 2) the asymptotically best estimator is robust against the deviation of the population eigenvalues from the block-wise infinite dispersion