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The video discusses complete statistics in parameter estimation where a statistic t is defined as a function of data following a distribution. If the expected value of every function of the statistic equals zero for all parameter values, the statistic is complete. Even if it's true for all but one point (with probability zero), it's still considered complete. For example, x_n (nth order statistic) is shown to be sufficient and complete when x_i is from a given family of distributions indexed by a parameter theta.