Abstract

Quadratic inference function (QIF) analysis is more efficient than the generalized estimating equations (GEE) approach when the working covariance matrices for the data are misspecified. Since QIF naturally requires a weighting matrix which is the inverse of a sample covariance matrix of non-identically distributed data, finite sample performance can be greatly affected when the number of independent data points is not large enough, which is usually the case in cluster randomized trials or many longitudinal studies. While nonlinear shrinkage is very successful in regularizing the extreme eigenvalues of a sample covariance matrix, the method is only restricted to independent and identically distributed data. We propose a novel nonlinear shrinkage approach for a sample covariance matrix of non-identically distributed data, which improves finite sample performance of QIF , and gives room for increasing the potential number of working correlation structures for even better performance. Together with a nonlinearly shrunk weighting matrix, we derive the asymptotic normality of the parameter estimators, and give an estimator for the asymptotic covariance matrix. We demonstrate the performance of the proposed method through simulation experiments and a real data analysis.