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

Failure prediction of Chinese A-share listed companies : comparisons using logistic regression model and neural network analysis : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey University, Palmerston North, New Zealand

This study compares the relative prediction accuracy of corporate failure between two prediction methods –logistic regression model and neural network analysis– based on a sample of 3598 observations and companies data obtained from the Chinese A- Share market during the period 1991 to 2002. Seven criteria have been set up to define failure according to attributes of Chinese listed companies. Using forty financial ratios and seven misclassification cost ratios of Type I and Type II error, two models achieve ranges of minimal misclassification cost at optimal cut-off points for two years prior to business failure; The logistic regression model is slightly superior to neural network analysis. Compared with random prediction, both models are efficient. In addition, the study points out that Total Asset Turnover (TATR), Cash Ratio (CASR), Earning per Share (EPS), Total Debt to Total Asset (TDTA), Return on Assets (ROA) and the natual log of Total Market Value (MVLN) could be significant financial indictors of corporate failure. Results of the study have important implications in credit evaluation, internal risk control and capital market investment guidelines