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

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

MAP7D2 is a brain expressing X-linked maternal imprinted gene in humans

Increasing evidence suggests imprinted genes influence mouse and human behaviors and cognitive functions. Unlike autosomal imprinted genes, X-linked imprinted genes are expressed in a sex-dependent manner because of male hemizygosity. Therefore, these genes could directly affect sex-specific brain functions and sex-biased vulnerability to psychiatric disorders such as autism1. Comparing lymphoblastoid cell lines (LCL) and peripheral blood mononuclear cells (PBMC) from healthy adult male and females, we identified MAP7 domain containing 2 (MAP7D2) as the first human X-linked imprinted gene. Both in LCL and PBMC, MAP7D2 expression was significantly suppressed in males by maternal imprinting. In each female LCL clone, MAP7D2 was expressed higher in paternally derived allele and was affected by X-chromosome inactivation. In female PBMC, however, reactivation of maternal MAP7D2 alleles was observed. MAP7D2 was expressed specifically in the brain among human tissues with unique isoforms. These results predict a crucial role of MAP7D2 for human sex-dependent neurobiological traits

Conditioning Information and Variance Bounds on Pricing Kernels with Higher-Order Moments: Theory and Evidence

The author develops a strategy for utilizing higher moments and conditioning information efficiently, and hence improves on the variance bounds computed by Hansen and Jagannathan (1991, the HJ bound) and Gallant, Hansen, and Tauchen (1990, the GHT bound). The author's bound incorporates variance risk premia. It reaches the GHT bound when non-linearities in returns are not priced. The author also provides an optimally scaled bound with conditioning information, higher moments, and variance risk premia that improves on the Bekaert and Liu (2004, the BL bound) optimally scaled bound. This bound reaches the BL bound when nonlinearities in returns are not priced. When the conditional first four moments are misspecified, the author's optimally scaled bound remains a lower bound to the variance on pricing kernels, whereas the BL bound does not. The author empirically illustrates the behaviour of the bounds using Bekaert and Liu's (2004) econometric models. He also uses higher moments and conditioning information to provide distance measures that improve on the Hansen and Jagannathan distance measures. The author uses these distance measures to evaluate the performance of asset-pricing models. Some existing pricing kernels are able to describe returns ignoring the impact of higher moments and variance risk premia. When accounting for the impact of higher moments and variance risk premia, these same pricing kernels have difficulty in explaining returns on the assets and are unable to price non-linearities or higher moments.Financial markets; Market structure and pricing