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半正态图最大值的渐近理论
We study approximations to the distribution of the largest Walsh-Fourier coefficient obtained by transforming i.i.d. observations from a non-normal parent distribution. The study is inspired by the use of half-normal plots in screening studies and in the analysis of molecular sequence data. In the latter context, we indicate why continuity corrections are needed.
针对随机序增大备择的稳健序贯监测方案
We sequentially observe independent observations $X_1, X_2,\ldots$ such that initially they have distribution $G_0$; at some unknown time $\nu$ they become stochastically larger, having distribution $G_1$. Neither $G_0$ nor $G_1$ is fully specified. We wish to detect that a change has taken place as soon as possible after its occurrence, subject to a constraint on the rate of false alarms. We derive a family of nonparametric sequential procedures based on ranks, with…
分布变化检测的高效序贯非参数方案
Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is…
序列匹配的极值理论
Consider finite sequences $X_1, X_2,\cdots, X_m$ and $Y_1, Y_2,\cdots, Y_n$ where the letters ${X_i}$ and ${Y_i}$ are chosen i.i.d. on a countable alphabet with $p=P(X_1=Y_1)\in(0,1)$ We study the distribution of the longest contiguous run of matches between the X's and Y's allowing at most k mismatches. The distribution is closely approximated by that of the maximum of (1 - p)mn i.i.d. negative binomial random variables. The latter distribution is in turn shown to behave…
大规模有限总体中的逐次抽样
The permutation distribution induced upon a finite population by the order of selection under successive sampling is closely related to the order statistics of independent exponentially distributed waiting times. This characterization is applied to obtain necessary and sufficient conditions for asymptotic normality of the sum of characteristics observed in a successive sample from a finite population. The necessary and sufficient conditions generalize previous results for…
分类问题的渐近有效解
We study a class of decision rules based on an adaptive partitioning of an Euclidean observation space. The class of partitions has a computationally attractive form, and the related decision rule is invariant under strictly monotone transformations of coordinate axes. We provide sufficient conditions that a sequence of decision rules be asymptotically Bayes risk efficient as sample size increases. The sufficient conditions involve no regularity assumptions on the underlying…
子抽样中的完全分离组
We study several combinatorial problems related to the choice of groups of subsets to be used in the subsampling procedure of Hartigan (J. Amer. Statist. Assoc. 1969). The complete separation property is shown to guarantee asymptotic efficiency relative to $t$. Problems associated with the relative variance criterion are discussed.