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聚焦贝叶斯方法：导言AI 解读

This special section of the Theory and Methods section of the Journal of the American Statistical Association honors Morris H. DeGroot, who died November 2, 1989. It contains his last paper, which was being written at the time of his death. Morrie DeGroot was the founding editor of Statistical Science, which published an issue (Vol. 6, No. 1) in 1991 in his honor. That issue contains an excellent biography of Morrie. Morrie was, of course, a Bayesian. This special section is…

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保序、凸及相关样条AI 解读

In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence and characterization theorem for isotonic or convex splines. Two special cases are examined showing the existence of a globally monotone cubic smoothing spline and a globally convex quintic…

关于若干递归概率密度估计量的讨论AI 解读

The density estimator, $f^\ast_n(x) = n^{-1}\sum^n_{j = 1}h^{-1}_jK((x - X_j)/h_j)$, as well as the closely related one $f^\dagger_n(x) = n^{-1}h_n^{-\frac{1}{2}}\sum^n_{j = 1}h_j^{-\frac{1}{2}}K((x - X_j)/h_j)$ are considered. Expressions for asymptotic bias and variance are developed. Using the almost sure invariance principle, laws of the iterated logarithm are developed. Finally, illustration of these results with sequential estimation procedures are made.

指数族中序约束的似然比检验AI 解读

This paper considers likelihood ratio tests for testing hypotheses that a collection of parameters satisfy some order restriction. The first problem considered is to test a hypothesis specifying an order restriction on a collection of means of normal distributions. Equality of the means is the subhypothesis of the null hypothesis which yields the largest type I error probability (i.e., is least favorable). Furthermore, the distribution of $T = -\ln$ (likelihood ratio) is…

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