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摘要暂缺

Cramér–von Mises 统计量的分量（二）AI 解读

Summary Let θ^ be an asymptotically efficient estimator of parameter vector θ based on an ordered sample of n independent observations y 1, ..., y n from a distribution with distribution function F(y, θ) and let x^j=F(yj,θ^), j = 1, ..., n. Let Ŵn 2 be the Cramér–von Mises statistic calculated from ◯ 1, ..., ◯ n. This paper shows how to construct components ẑ n1, ẑ n2, ... such that Ŵ n 2 = ∑j=1 ∞ μj ẑ nj 2 where ẑ n1, ẑ n2, ... are asymptotically independent N(0, 1)…

摘要暂缺

Cramér–von Mises 统计量的分量：第一部分AI 解读

Summary Let Fn(x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér-von Mises statistic Wn2 in the form ∑j=1∞(jπ)−2znj2 where the znj are the principal components of n{Fn(x)−x}. It is shown that the znj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their…