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A model that accounts for uncertain data dependency is developed by generating a large class of stationary stochastic processes, each with the same univariate distribution. This class can be considered to be a contamination class about the nominal independent and identically distributed (i.i.d.) process distribution. The class is developed specifically for application to robust detector and estimator design based on asymptotic variance. Application of this dependency class leads to an intuitively pleasing result: the minimax variance estimators and the maximin efficacy detectors are the same as obtained using i.i.d, asymptotic estimation and detection theory. Thus our technique generalizes previously obtained robust design results for i.i.d, data to this dependent data case.