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We present a theoretical framework for the linear collusion analysis of watermarked digital video sequences, and derive a new theorem equating a definition of statistical invisibility, collusion-resistance, and two practical watermark design rules. The proposed framework is simple and intuitive; the basic processing unit is the video frame and we consider second-order statistical descriptions of their temporal inter-relationships. Within this analytical setup, we define the linear frame collusion attack, the analytic notion of a statistically invisible video watermark, and show that the latter is an effective counterattack against the former. Finally, to show how the theoretical results detailed in this paper can easily be applied to the construction of collusion-resistant video watermarks, we encapsulate the analysis into two practical video watermark design rules that play a key role in the subsequent development of a novel collusion-resistant video watermarking algorithm discussed in a companion paper.