Orthogonal bases approach for comparing nonnormal continuous distributions

We present an orthonormal bases approach for detecting general differences among continuous distributions. An unknown density function is represented by a finite vector of its estimated Fourier coefficients with respect to a suitable orthonormal basis. For a wide class of orthonormal bases, we establish asymptotic normality of the vector of estimated Fourier coefficients and propose an unbiased and consistent estimator of its asymptotic covariance matrix. Fourier coeffients are modelled as functions of fixed and possibly random effects. This approach allows simultaneous detection of distributional differences attributable to various factors in clustered and correlated data with suffciently large numbers of observations per each cluster with the same fixed and random effects realisations. This work was motivated by multi-level clustered non-Gaussian datasets from genetic studies. Copyright 2005, Oxford University Press.