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In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Z i and the general link function, under the most general assumption on the minimum eigenvalue of n i=1 Z i Z i , the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

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