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In generalized linear models with fixed design, under the assumption λ n → ∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator β n , which is the root of the quasi-likelihood equation with natural link function n i=1 X i (y i − μ(X i β)) = 0, is obtained, where λ n denotes the minimum eigenvalue of n i=1 XiX i , Xi are bounded p × q regressors, and yi are q × 1 responses.

The aim of this paper is to develop Cook's distance measures for assessing the influence of both atypical curves and observations under varying coefficient model for functional responses. Our Cook's distance measures include Cook's distances for deleting multiple curves and for deleting multiple grid points, and their scaled Cook's distances. We systematically investigate some theoretical properties of these diagnostic measures. Simulation studies are conducted to evaluate the finite sample properties of these Cook's distances under different scenarios. A real diffusion tensor tract data set is analyzed to illustrate the use of our diagnostic measures.

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