GEE analysis of clustered binary data with diverging number of covariates

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this "large $n$, diverging $p$" framework, we provide appropriate regularity conditions and establish the existence, consistency and asymptotic normality of the GEE estimator. Furthermore, we prove that the sandwich variance formula remains valid. Even when the working correlation matrix is misspecified, the use of the sandwich variance formula leads to an asymptotically valid confidence interval and Wald test for an estimable linear combination of the unknown parameters. The accuracy of the asymptotic approximation is examined via numerical simulations. We also discuss the "diverging $p$" asymptotic theory for general GEE. The results in this paper extend the recent elegant work of Xie and Yang [Ann. Statist. 31 (2003) 310--347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522--541] in the "fixed $p$" setting.Comment: Published in at http://dx.doi.org/10.1214/10-AOS846 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Power spectrum of the fluctuation of Chebyshev's prime counting function

The one-sided power spectrum of the fluctuation of Chebyshev's weighted prime counting function is numerically estimated based on samples of the fluctuating function of different sizes. The power spectrum is also estimated analytically for large frequency based on Riemann hypothesis and the exact formula for the fluctuating function in terms of all the non-trivial Riemann zeroes. Our analytical estimate is consistent with our numerical estimate of a 1/f^2 power spectrum

Heterogeneity, Politics of Ethnicity, and Multiculturalism What is a Viable Framework for Indonesia?

Indonesia is a plural society that consists of several hundred ethnic and sub-ethnic groups. One of its generic characteristics is heterogeneity. In the last ten years after the implementation of regional autonomy, we have witnessed the emergence of strong ethnic and religiously flavoured local identity politics in various places in Indonesia that created open and vicious conflicts. This periodical violence exploded especially during the election of district and provincial heads. The intimate relation multiculturalism, with the actual political praxis of everyday life as an alternative to the existing paradigm of the “homogenization” of nationhood, has not been discussed. I believe it is time to discuss the strategic junctures between heterogeneity, politics of ethnicity (and religion) and multiculturalism as well as their possible realization at the local and national levels in order to find a viable framework for a future Indonesia