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408 Buried treasuresIn a most rewarding collaboration, David Mason and I tackled the casewhere the W n,i were exchangeable, making the seemingly superfluous observationthat ¯X W n must have the same conditional distribution, given data X i ,as the additionally randomizedT n = 1 nn∑W n,πn,i X i ,i=1where, for each n, π n,i is a uniform random permutation of the integers1,...,n.Whiletheusualbootstrapstatistichastwosourcesofrandomness(one from the data and from the bootstrap weights), this T n had yet a thirdsource, neither generated by nature or the statistician, but just imagined owingto the exchangeability of the weights. Having all three sources allowed usto condition on both the data X i and the statistician-generated weights W n,i ,and still have some randomness in T n .A quite unconnected and somewhat amazing treasure from the theory oflinear rank statistics now became relevant. Given two triangular arrays ofconstants, a n,i and b n,i ,therandomizedmeanS n =n∑a n,πn,i b n,ii=1had been studied extensively in nonparametric testing, because this is theform of the linear rank statistic. Hájek (1961) presented weak conditions onthe triangular arrays such that S n is asymptotically normal, owing to therandom shuffling caused by the π n,i . Thus, reconsidering Hájek’s result inthe new bootstrap context was the key to making progress on the weightedbootstrap problem (Mason and Newton, 1992).36.1.3 Cancer genetics and stochastic geometryAtumorismonoclonalinoriginifallitscellstracebydescenttoasingleinitiatedcell that is aberrant relative to the surrounding normal tissue (e.g., incurssome critical genetic mutation). Tumors are well known to exhibit internalheterogeneity, but this does not preclude monoclonal origin, since mutation,clonal expansion, and selection are dynamic evolutionary processes occurringwithin a tumor that move the single initiated cell to a heterogeneous collectionof descendants. Monoclonal origin is the accepted hypothesis for mostcancers, but evidence is mounting that tumors may initiate through some formof molecular interaction between distinct clones. As advanced as biotechnologyhas become, the cellular events at the point of tumor initiation remainbeyond our ability to observe directly, and so the question of monoclonal versuspolyclonal origin has been difficult to resolve. I have been fortunate towork on the question in the context of intestinal cancer, in series of projectswith W.F. Dove, A. Thliveris, and R. Halberg.